SOLUTION: What is the surface area of a prism whose bases are right triangles? The side measures are 2 meters, 3 meters, and 4 meters, and the height is 5.

Question 462726: What is the surface area of a prism whose bases are right triangles? The side measures are 2 meters, 3 meters, and 4 meters, and the height is 5.
Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!
What is the surface area of a prism whose bases are right triangles? The side measures are 2 meters, 3 meters, and 4 meters, and the height is 5.
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If I read your problem correctly, this is a right triangular prism with a height of 5. The side measures the triangular base are 2 meters, 3 meters, and 4 meters.
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We cannot have a right triangle with those measurements because the Pythagorean Theorem does not hold...2-squared plus 3-squares does not equal 4-squared. I think you might be that the measures of the side measures of the triangle are 3m, 4m, and 5m, and the height is 2 m.
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That's the problem I'll solve. If this is not the case, you can resubmit or send me a message.
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To find the surface area, we need to calculate the area of the two bases, as well as the area of the three sides.
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The formula for the area A of a right triangle is
A = (1/2)*b*h
where b is the base and h is the height. Using the values given in the modified problem, we have
A = (1/2)(3)(4) = 6
So the area of each triangle base is 6 square meters.
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Now we need the area of each side of the prism. The shapes of the sides are rectangles measuring
3 by 2 square meters
4 by 2 square meters
5 by 2 square meters
The formula for the area A of a rectangle is s*h here s is the side length of the triangle, and h is the height of the prism. (This is just a variation on area=length times width.)
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The rectangles measure
(3)(2) = 6 square meters,
(4)(2) = 8 square meters, and
(5)(2) = 10 square meters.
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Now we just add up the area of each face of the prim to get the surface area SA.
SA = 6 + 6 + 6 + 8 + 10 = 36 square meters.
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hope this helps!
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Ms.Figgy
math.in.the.vortex

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