Question

What is the surface area of this design?

Answer 1

Answer:  The correct option is (C) 197 in².

Step-by-step explanation:  We are given to find the surface area of the design shown in the figure.

We can see that

the design consists of 2 trapezoids and 4 rectangles.

Now, the surface area of the whole design will be the sum of the area of these 6 two-dimensional figures.

Area of 2 trapezoids is given by

$A_t=2\times \dfrac{1}{2}\times\textup{sum of parallel sides}\times\textup{height}\\\\\\\Rightarrow A_t=(5+9)\times5\\\\\Rightarrow A_t=70~\textup{in}^2.$

And the area of the 4 rectangles is given by

$A_r=5\times5+5\times5+5\times6.4+5\times9\\\\\Rightarrow A_r=25+25+32+45\\\\\Rightarrow A_r=127~\textup{in}^2.$

Therefore, the total surface area of the given design is

$S=A_t+A_r=70+127=197~\textup{in}^2.$

Thus, the correct option is (C) 197 in².

Answer 2

The correct answer is C or 197in squared because the back and top sides are 25. so that is 50. Then the sides are 35. so that is 70. and the front is 32. The bottom is 45. So, 50+70+32+45 is 197in squared.