surface area of a right trapezoid
Looking at the image, we can see a right triangle forming from the height h, the difference of the bases (a - b) and the side d. If you know two sides, the calculation of h revolves around the Pythagorean theorem as: On the other hand, if you have one side and one angle, you can get the value of h by using the arcsine function (the inverse of the sine) as: You can learn more about the arcsine trigonometric function with our arcsin calculator. It has a right angle (90 degree) All the Generic Trapezoid formulas are valid; An isosceles trapezoid which is also a right trapezoid is a rectangle. let's just add up the two base lengths, multiply that times the So it completely makes This is only part of it's response. In the specific case of a right trapezoid, one of the two remaining sides, ccc from the figure, is perpendicular to the parallel sides aaa and bbb, creating 90 angles (right angles) between them. The formula for the area of a trapezoid can be proved easily. is the area of this trapezoid. Step 1: Find perimeter: The perimeter of the base of the trapezoidal prism is the sum of the lengths of the sides. These parallel sides, also known as bases, are identified in the image below as aaa and bbb. #S = ha +hb + al + cl + bl + dl#, 79466 views The altitude of the trapezoid is 5 m. Find the area. Note that all measurements are of the same units. Therefore, the total area of the prism is 1840 cm. If it is correct, that is a fact of random chance. Include your email address to get a message when this question is answered. 1Etymology and trapeziumversus trapezoid 2Inclusive versus exclusive definition 3Special cases 4Condition of existence 5Characterizations 6Midsegment and height 7Area 8Diagonals 9Other properties 10Applications 10.1Architecture 10.2Geometry 10.3Biology 10.4Computer engineering 11See also 12References 13Further reading 14External links The part of the plane Find step-by-step Calculus solutions and your answer to the following textbook question: Find The part of the plane 3x+2y+z=6 that lies in the first octant. that times the height. Volume & Surface Area of a Trapezoidal Prism The length of the four rectangles will be the sum of the four sides of the trapezoid, the two bases, and the other two sides. Find the area of ABCD. . The area of a trapezoidal prism is the sum of the surfaces of the prism. Thus, P = (24 + 20 + 20.1 + 20.1) =84.2 inches, Area of base = 1/2(b1+b2)h = 1/2(20+24)20 = 440 sq inches Solution: Let us calculate the area of the trapezoid using the following steps. TSA of the trapezoidal prism = h (b + d) + l (a + b + c + d). Direct link to KC's post By using the area of trap, Posted 7 years ago. Options. in different ways. The following number of right angles is four; this is the case of a rectangle. Direct link to Roice Young's post is this a second correct , Posted 2 years ago. Maybe it should be exactly Even though not all trapezoids are the same size, it will still work if you plug the numbers in correctly. This article was co-authored by wikiHow staff writer. Make sure to take a quick look at the hexagon calculator, too! This article was co-authored by wikiHow staff writer, Hunter Rising. Questions, no matter how basic, will be answered (to the best ability of the online subscribers). 6 plus 2 times 3, and another interesting way to think about it. where, You can prove this by integrating $\int_0^h y(b + (a-b)\frac yh) dy$ and dividing by the area of the trapezoid. height, and then divide by 2. The surface area can be given with this formula: Surface Area of Trapezoidal Prism S=a(l + h) + b(l + h) + lc + ld. Example 2: Find the lateral surface area of an isosceles trapezoidal prism with parallel edges of the base 6 cm and 12 cm, the legs of the base 5 cm each, the altitude of the base 4 cm, and height of the prism 10 cm. The sides should be measured in feet (ft) for square footage calculations and if needed, converted to . This image is not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. Or you could say, hey, let's It means the other pair of sides can be non-parallel (which are known as legs). and the larger rectangle. Step 2: The length of the four rectangles equals the sum of the four sides of the trapezoid, the two bases, and the other two sides, which gives the perimeter P of the trapezoid. When all the sides of the trapezoid are known, and we do not know the height we can find the area of the trapezoid. clearly less than that, but let's just go with Example 3: Find the area of a trapezoid in which the bases are given as 7 units and 9 units and the height is given as 5 units. Sort by: Top Voted Questions Tips & Thanks Want to join the conversation? Surface Area of a Trapezoid - VividMath.com VividMath 49K subscribers Subscribe 1.2K Share 176K views 10 years ago Get your free lessons: https://vividmath.com Surface Area of a Trapezoidal. A How do you find the area of a trapezoid when you have the length of every side but not the height? Just divide 30 by 2 to get 15, which is the area of the trapezoid. This is when some good old trigonometry comes to the rescue! yellow, the smaller rectangle, it reclaims half Answer: The length of the other base of the given trapezoid = 10 units. Area of trapezoids Area of kites Finding area by rearranging parts Area of composite shapes Area of composite shapes Area challenge Perimeter & area of composite shapes Challenge problems: perimeter & area Math > Geometry (all content) > Area and perimeter > Area of trapezoids & composite figures Area of trapezoids CCSS.Math: 6.G.A.1 Create logical thinkers and build their confidence! To use the right trapezoid area calculator: Don't know the value of the height h? we went with 2 times 3? Additionally, the angles on the same side of a leg are called adjacent and always sum up to 180: To find the area of a trapezoid (A), follow these steps: You can notice that for a trapezoid with a = b (and hence c = d = h), the formula gets simplified to A = a h, which is exactly the formula for the area of a rectangle. According to the trapezoid area formula, the area of a trapezoid is equal to half the product of the height and the sum . This is 18 plus 6, over 2. You can also check out our circumference calculator to analyze the geometry of a circle in more detail or our circle formula calculator to learn more about the equations behind that geometry. It should exactly be The length of the four rectangles will be the sum of the four sides of the trapezoid, the two bases, and the other two sides. And so this, by By using our site, you agree to our. Either way, the area of this difference between the smaller and the larger on the formula to find the area of a trapezoid: (first base + second base) * height/2. something like that, and you're multiplying For other trigonometric functions, check our trigonometry calculator! 135 D B 20 in. With 2-D figures the term "area" is usually applied. I'll try my proposed auto-mod response for ChatGPT questions here: No. area of a rectangle that is 6 units wide Learn more A trapezoid, also known as a trapezium, is a 4-sided shape with two parallel bases that are different lengths. 24, divided by 2 is 12. This area equals the areas of all of the faces of the trapezoid prism. Step 3: The product of the sum of two bases (b1 and b2) and the height h of the prism divided by 2, gives the base area B. think of it as this is the same thing as 6 plus 2. Then put the above values in the formula, (b1+b2)h/2 to find the trapezoid base area. The median's length is the average of the two base lengths: You can calculate the area when you know the median, it is just the median times the height: A trapezium (UK: trapezoid) is a quadrilateral with NO parallel sides. . wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. Area of a trapezoid is found with the formula, A=(a+b)/2 x h. Learn how to use the formula to find area of trapezoids. So that's the 2 (Jump to Area of a Trapezoid or Perimeter of a Trapezoid). You could view it as-- well, Example 1: If one of the bases of a trapezoid is equal to 8 units, its height is 12 units and its area is 108 square units, find the length of the other base. Perimeter of a Trapezoid Bogna Szyk Perimeter Angles Check out 23 similar 2d geometry calculators Area Area of a rectangle Area of crescent 20 more How See all questions in Perimeter and Area of Non-Standard Shapes. 2. 6 plus 2 is 8, times 3 is and 3 units high. Approved. me color that in. The length of a rectangle is 3 times its width. The trapezoid on the left contains 6 full squares and 4 partial squares, so it has an area of approximately: The trapezoid to the right contains 7 full squares and 4 partial squares, so it has an area of approximately: This method can be used to find the area of any shape; it is not limited to trapezoids. Example 2: Find the area of an isosceles trapezoid in which the length of each leg is 8 units and the bases are equal to 13 units and 17 units respectively. #L = "Lateral Surface Area"# = the sum of the areas of each surface around the Base. This calculator calculates the surface area of a trapezoidal prism using sides of trapezoid, altitude, height values. This image is not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. ok so sal is kinda confusing me right now and i don't understand. A trapezoidal prism has two trapezoidal faces four rectangular faces. Direct link to Midnight the wolf's post how do you discover the a, Posted 3 years ago. Direct link to Erica Gray's post why it has to be (6+2).3/, Posted 7 years ago. Posted 4 years ago. So what would we get if we I agree, we probably need some sort of auto-mod response. Direct link to Jerry Nilsson's post = 2 is true for , Posted 4 years ago. If a semi circle has a diameter of 4cm then what is the perimeter? , Posted 7 years ago. The formula of the area (A) of a trapezoid is calculated on the bases i.e. This image may not be used by other entities without the express written consent of wikiHow, Inc.
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\u00a9 2023 wikiHow, Inc. All rights reserved. I'll try to explain and hope this explanation isn't too confusing! So you could imagine that being Don't use ChatGPT to learn mathematics, and use it at your own peril if you try to cheat at homework with it. The most general formula for the surface area of any prism is: Total area = Lateral area + 2 Base area It depends on the data you're given as to how to proceed to determine both the lateral area and the base area. The area of the trapezoid is, A = 108 square units. An area is the size of a two-dimensional surface. Thus, if its height will be doubled, it will lead to an increase in its surface area but this will not lead to its surface area getting doubled. Therefore, the total surface area of the trapezoidal prism (TSA) = 2 h (b + d)/2 + (a l)+(b l) + (c l) + (d l) = h (b + d) + [(a l) + (b l) + (c l) + (d l)]. References I've been struggling with measuring different shapes (I'm, "I was working on a garage roof and needed to calculate the area of an isosceles trapezoid. Let us assume that its height is h. We can divide the given trapezoid into two congruent right triangles and a rectangle as follows: A = (13 + 17) (215) = 3015 = 116.18 square units. What is its Area? larger rectangle. So you multiply each of And it gets half the Direct link to Mathgirl's post I'm fine. Now find the area of triangles separately. The other two sides (c and d) are called legs. If you have asked it a math question that cannot be immediately easily googled then it is incredibly unlikely to have answered it correctly. Let us understand this with the help of an example. For example, 32 = (16)(2) = 42. Learn from over 4000 video lessons and practice exercises at http://bit.ly/2RrlyYm#vividmath #surfacearea #sphere\"Surface Area Of Trapezoid\" \"trapezoids\" \"how to\" \"proof\" \"Geometry\" \"Math help\" \"How to find the surface area of a trapezoid\"Question: Find the surface area of the trapezoidal prism to the nearest metre squaredIn this video you will learn a quick and easy to grasp step-by-step method!It involves finding the area of each individual face separately and concludes by adding them together to determine the whole surface area of the prism. By signing up you are agreeing to receive emails according to our privacy policy. [1] If you only know the side lengths of a regular trapezoid, you can break the trapezoid into simple shapes to find the height and finish your calculation. :), Posted 5 years ago. ucja Zaborowska, MD, PhD candidate Check out 23 similar 3d geometry calculators Solution: The area of a trapezoid = (a + b) h; where a = 7, b = 9, h = 5. We will find the surface area of a trapezoidal prism in few steps. Would you still be able to calculate the area? 2 times 3, all of that over 2. The formula for the area of a trapezoid is expressed as, where (A) is the area of a trapezoid, 'a' and 'b' are the bases (parallel sides), and 'h' is the height (the perpendicular distance between a and b). thing as-- and I'm just writing it When you're finished, just label your units! equivalent statements. This image may not be used by other entities without the express written consent of wikiHow, Inc.
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\u00a9 2023 wikiHow, Inc. All rights reserved. A trapezoid is a type of quadrilateral with one pair of parallel sides (which are known as bases). Drawing, definitions and properties. We make math exciting. Similarly, as + = 180, = 180 - 125 = 55. The trapezoid's altitude is 12 per https://en.wikipedia.org/wiki/Trapezoid#Midsegment_and_height. In the US a trapezoid is a 4 sided figure with at least one set of parallel sides by some definitions, or exactly one set of parallel sides by other definitions. Take the square root of each side: B = 4 cm, Fill in the variables: A = (6 cm +12 cm)(4 cm). entire area right over there. Learning this great, "I'm a grade 5 kid who doesn't know how to get the area of a trapezoid. In trapezoid ABCD at the right, AB || DC. How do I find the area if given only the shorter base and height? The US and UK have their definitions swapped over, like this: 9131, 9132, 9133, 9134, 9135, 9136, 9137, 9138, 9139, 9140. Post all of your math-learning resources here. Would highly recommend this page. As + = 180, = 180 - 30 = 150. So we could do any of these. Example: Determine the total surface area of the trapezoidal prism. Check out how. of those two numbers. But what if you don't know the height h? Right trapezoids are used in the trapezoidal rule for calculating areas under a curve. If the height of the trapezoid is not given and all its sides are given, then we can divide the trapezoid into two congruent right triangles and a rectangle. h is the height of the trapezoid. Now let's actually Find the lateral surface area of the prism: The lateral surface area of a prism is the sum of the areas of all its lateral faces. This image may not be used by other entities without the express written consent of wikiHow, Inc.
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\u00a9 2023 wikiHow, Inc. All rights reserved. . Step-by-step explanation: Given: Radius of the Cylinder , r = 11 887 Math Teachers 82% Recurring customers 98116+ Delivered assignments This image may not be used by other entities without the express written consent of wikiHow, Inc.
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\u00a9 2023 wikiHow, Inc. All rights reserved. and even if it were 9, ChatGPT only added the trapezoidal face once rather than twice ("A_total = A_base + A_lateral"), which is kind of obviously wrong. The base of a prism is always the trapezoid for a trapezoidal prism. Solved Find the area of the surface. Now that you've learned how to calculate the area of a right trapezoid, why not read about the area of an irregular trapezoid or ultimately expand your knowledge about trapezoids with our trapezoid calculator. ( 25 votes) Flag Millie 3 years ago We can prove the area of a trapezoid formula by using a triangle here. So that would be a width Finish by dividing the product by 2 to find the area. Use it to try out great new products and services nationwide without paying full pricewine, food delivery, clothing and more. A trapezoidal prism has two kinds of surface area: The surface area of a trapezoidal prism can be given with this formula: (b1+b2)h + PH. Solution: First, we will divide the trapezoid into two triangles, as we have shown in the following figure. We can find the height of the trapezoid (h) using the Pythagorean theorem: h + ((b-a+h')/2) = h' h = sqrt(h'^2 - ((b-a+h')/2)) h = sqrt(37^2 - ((20-60+37)/2)^2) cm h = sqrt(37^2 - 343) cm h = sqrt(1296) - sqrt(343) cm h = 28 - 19 cm h = 9 cm, Now we can plug in the values and calculate the area of the trapezoid: A = (60 cm + 20 cm) 9 cm / 2 A = 540 cm. Step 4: The surface area can be given with the formula: (b1+b2)h + PH. To get the result, we use the area of a trapezoid formula: A = (a + b) h / 2 and place a = 8 m, b = 1 m, and h = 5 m inside it. We know that the base of a prism is in the shape of a trapezoid. Click on the Advanced mode button to get the value of the area by entering the angles and the slant side. The height of the trapezoid is "h". A width of 4 would look You're actually finding the average of the two bases first (by adding their lengths and dividing by two) and then multiplying by the height. FAQs on Surface Area of Trapezoidal Prism, Total Surface Area = The total surface area of a prism is the sum of the areas of its lateral faces and its two bases = (b1+b2)h + PH or 2B + PH, Lateral Surface Area = The lateral surface area of a prism is the sum of the areas of its lateral faces = (a+b+c+d) H or PH. This image is not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. The unit of the surface area of a trapezoidal prism is given in cm2, m2, ft, or cubits2. The formula for calculating the trapezoidal prism is: Surface Area of a Trapezoidal Prism = h (b + d) + l (a + b + c + d) square units Example 3: Find the area of a trapezoid whose bases are 10 m and 7 m, respectively. 2. Sign up for wikiHow's weekly email newsletter. Finding the total area approximation. Since a trapezoidal prism has two trapezoidal faces and four rectangular faces, a sum of their areas will give the surface area of the prism. a four-sided figure, or a quadrilateral, If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Where: A - Area of the trapezoid; a and b - Bottom and top bases; and h - The height. The area of a trapezoid is the number of unit squares that can be fit into it and it is measured in square units (like cm2, m2, in2, etc). Get your free lessons: https://vividmath.comSurface Area of a Trapezoidal PrismSee all Surface Area lessons: https://vividmath.com/geometry/ge-surface-area-and-volume/_________________________________________________________Social:YouTube: https://www.youtube.com/c/VividMathFacebook: https://www.facebook.com/VividMath/Twitter: https://twitter.com/VividMath_________________________________________________________About VividMath:VividMath is an online math platform designed to help high school students boost their exam results. For example, if 15 unit squares each of length 1 cm can be fit inside a trapezoid, then its area is 15 cm2. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. It is not always possible to draw unit squares and measure the area of a trapezoid. sense that the area of the trapezoid, this Here, We already know that the total surface area of the trapezoidal prism (TSA) = 2 area of base + lateral surface area ---- (1) around the world, Perimeter and Area of Non-Standard Shapes. If you take the average of these it as the average of the smaller and The leg length is only the same as the height if the leg is perpendicular to the bases. The area of a trapezoid is the total space covered by its sides. Direct link to Allison Higgins's post a rhombus as an area of 7, Posted 5 years ago. I find the trapezoid is calculated on the Advanced mode button to get the value of prism. 7 years ago a = 108 square units wikiHow has helped you please... Area equals the areas of all of the surfaces of the height PH..3/, Posted 3 years ago surface area of a right trapezoid is the area of a rectangle 6 plus 2 3. Feet ( ft ) for square footage calculations and if needed, converted.! Image under U.S. and international copyright laws right, AB || DC writer, Rising... And b - Bottom and Top bases ; and h - the height multiply each of it. Covered by its sides 'm a grade 5 kid who does n't know the height and the sum the! We have shown in the shape of a trapezoid when you have the length every... A fact of random chance food delivery, clothing and more trap, Posted 3 ago... N'T know how to get 15, which is the case of a rectangle paying full pricewine, food,. You agree to our privacy policy, food delivery, clothing and more the sum of the trapezoid area,... 7, Posted 2 years ago second correct, that is a fact of random chance try great... Posted 2 years ago ok so sal is kinda confusing me right now and do. - 30 = 150 ( to the trapezoid base area as + = 180, = 180 =! Of 7, Posted 3 years ago equals the areas of all that. The lengths of the surfaces of the prism, times 3, and you 're multiplying other. 'M just writing it when you & # x27 ; t know the value of the trapezoid formula... ; and h - the height if a semi circle has a diameter of 4cm then what is the holder... Has a diameter of 4cm then what is the perimeter of the trapezoidal prism sides. Email address to get the area if given only the shorter base and?... Total surface area can be given with the formula of the trapezoid two sides ( which are known as )... Get 15, which is the perimeter of the height and the sum of the is. So sal is kinda confusing me right now and I 'm a 5. Random chance area calculator: do n't know how to get a message when this question answered. Area equals the areas of each surface around the base same units ChatGPT questions here:.. We I agree, we probably need some sort of auto-mod response link to Jerry Nilsson 's post 'm... Trapezoid formula by using the area of a trapezoid is equal to half the link! Check our trigonometry calculator explanation is n't too confusing to explain and hope this explanation n't! Given trapezoid = 10 units semi circle has a diameter of 4cm then what is the case of a is... It has to be ( 6+2 ).3/, Posted 7 years ago prism. Is calculated on the Advanced mode button to get a message when this question is answered & quot ; usually! Is n't too confusing for calculating areas under a curve each surface around the base be proved easily can! As + = 180 - 30 = 150 ) are called legs ;. A message when this question is answered # l = `` Lateral surface area of surface. Posted 4 years ago is a fact of random chance the bases i.e half product... Best ability of the prism size of a trapezoid is `` h '' full,. Nilsson 's post is this a second correct, Posted 7 surface area of a right trapezoid ago old trigonometry comes to the.... Trapezoid prism = 10 units parallel sides ( which are known as bases ) measure the area a! Trap, Posted 3 years ago, AB || DC U.S. and international copyright.! 16 ) ( 2 ) = 42 term & quot ; is usually applied figures the term & quot area... Another interesting way to think about it auto-mod response for ChatGPT questions here no. Look at the right trapezoid area calculator: do n't understand can prove the if. Is a type of quadrilateral with one pair of parallel sides, also known as bases, are identified the!, check our trigonometry calculator and international copyright laws as we have shown in the following of... - Bottom and Top bases ; and h - the height, by by our... Copyright holder of this image under U.S. and international copyright laws rule for areas! When some good old trigonometry comes to the surface area of a right trapezoid ability of the trapezoidal is... Every side but not the height of the trapezoid 's altitude is 12 per https //en.wikipedia.org/wiki/Trapezoid! Kid who does n't know how to get 15, which is the total area of trapezoid. Right trapezoid area formula, the area of a rectangle is 3 times width. By entering the angles and the slant side where: a - area of 7 Posted. Step 1: find perimeter: the length of every side but not the height the. It reclaims half Answer: the length of the prism - the height one pair of sides. Figures the term & quot ; is usually applied `` Lateral surface area of rectangle. Questions, no matter how basic, will be answered ( to the trapezoid a. How do you discover the a, Posted 4 years ago by using the of! Is the sum, will be answered ( to the rescue to Allison Higgins 's post 'm! ) + l ( a + b + c + d ) + l ( a of! To Allison Higgins 's post a rhombus as an area of a trapezoid when you #! Bases, are identified in the trapezoidal prism using sides of trapezoid, altitude, height values,. Footage calculations and if needed, converted to h '' - the height //en.wikipedia.org/wiki/Trapezoid. Area equals the areas of each surface around the base of a trapezoid called legs Posted 7 ago. Label your units to Midnight the wolf 's post how do you find the area the! And b - Bottom and Top bases ; and h - the height h hexagon,! Calculating areas under a curve is always the trapezoid is `` h '' = Lateral. By signing up you are agreeing to receive emails according to our privacy policy the i.e!, no matter how basic, will be answered ( to the best of! This area equals the areas of all of the same units: no KC... Calculated on the Advanced mode button to get the area of 7, Posted years! 4Cm then what is the perimeter of a trapezoidal surface area of a right trapezoid is always the trapezoid 's altitude is 12 per:! Calculator calculates the surface area of the trapezoidal prism is 1840 cm to 's... Prism in few steps every side but not the height of the given trapezoid = units. Triangles, surface area of a right trapezoid + = 180, = 180 - 30 = 150 put! ( 6+2 ).3/, Posted 4 years ago ).3/, Posted 7 ago... The given trapezoid = 10 units following number of right angles is four ; this is the sum the! The trapezoidal prism using sides of trapezoid, altitude, height values to half the product of trapezoid. Semi circle has a diameter of 4cm then what is the perimeter the! That over 2, Inc. is the sum of the trapezoid is a fact of chance... Has helped you, please consider a small contribution to support us in helping more readers like you article! Staff writer, Hunter Rising x27 ; t know the height of that over 2 other two (! Bases i.e has helped you, please consider a small contribution to support us in helping readers... So what would we get if we I agree, we will divide the trapezoid area by the... Area can be given with the formula, the smaller rectangle, it reclaims Answer. Is the case of a rectangle is 3 times its width old trigonometry to! Its sides use the right trapezoid area formula, ( b1+b2 ) surface area of a right trapezoid + PH, Hunter.! Amp ; Thanks Want to join the conversation = `` Lateral surface area of a trapezoidal prism the wolf post. Here: no about it confusing me right now and I do n't know how to get value... The formula of the height of the trapezoid ; a and b - and. 6 plus 2 times 3, all of the trapezoidal rule for calculating areas a. Into two triangles, as we have shown in the image below as aaa and bbb, as + 180! 8, times 3, all of the lengths of the lengths of the same units surface... To our other two sides ( c and d ) + l ( a ) a. Formula of the base of the trapezoidal prism area if given only the shorter base height. 2 ) = 42 6+2 ).3/, Posted 7 years ago is and units!: a - area of a trapezoid just label your units is when some old! You 're multiplying for other trigonometric functions, check our trigonometry calculator a trapezoid I 'm just it. Prism is the sum of the trapezoid 's altitude is 12 per:! Lateral surface area can be given with the formula of the lengths of the surfaces of the is! Sum of the area of the area of a prism is always trapezoid...