Question

the surface area of the right prism shown is ________ square inches .

Answer 1

First, lets find the area of the base of the prism:

In this case, the area is:

$A_1=25\cdot16=400in^2$

Then, we can find the area of the side that has the shape of a right triangle:

The area of this triangle is:

$A_2=\frac{20\cdot15}{2}=\frac{300}{2}=150in^2$

finally, the remainin face of the prism is a rectangle with the following measures:

Then the area of this rectangle is:

$A_3=20\cdot16=320$

Now, notice that the prism has two faces in the shape of the right triangle and two faces in the shape of a rectangle, then, the total area surface will be:

$\begin{gathered} A=A_1+2A_2+2A_3 \\ \Rightarrow A=400+2(150)+2(320)=400+300+640=1340 \\ A=1340in^2 \end{gathered}$

therefore, the surface area is 1340in^2