Question

What is the surface area of the prism? A. 138 yd2 B. 192 yd2 C. 264 yd2 D. 272 yd2

Answer 1

In order to find the area of the triangular prism, we need to find the area of each of the figures that make it up. It might help if you draw the triangles and rectangles that make up the prism individually.

Let's start with the two triangles at either end of the prism.

A = 1/2bh   Area of a triangle
A = 1/2(6)(8)   Substitute
A = 24   Multiply / Divide

We now know that the area of the triangle at the end of the prism is 24 yd². However, since there are two of these triangles, we'll need to multiply that by 2. So, in total, the area of the two triangles is 48 yd².

There are three more rectangles that we need to find the area for: the base of the prism, the vertical edge of the prism, and the slanted edge of the prism. 

A = lw   Area of a rectangle
A = (9)(10)   Area of the slanted edge
A = 90 yd²   Multiply

A = (9)(6)   Area of the base
A = 54 yd²   Multiply

A = (8)(9)   Area of the vertical edge
A = 72 yd²

We now have the area for both triangles and each rectangle. Now, all we have to do is add these together to get the total surface area!

72 + 54 + 90 + 48 = 264 yd²
Surface Area = 264 yd²

The answer is 264 yd², or answer choice C.