Question

Use a net to find the surface area of the right triangular prism shown below: A. 104 square feet
B. 412 square feet
C. 468 square feet
D.504 square feet

Answer 1

I'd say by rounding and similar techniques the answer is 468, though it doesn't say all the needed numbers.

Answer 2

Answer:  The correct option is (C) 468 sq. ft.

Step-by-step explanation:  We are given to use a net to find the surface area of the right-triangular prism shown in the figure.

Let us divide the net of the prism in three parts, a rectangle ABCD and two congruent right-angled triangles $T_1$ and $T_2$ as shown in the attached figure below.

From the figure, we note that

the length and width of the rectangle ABCD are as follows :

AD = 15 + 9 +12 = 36 ft

and

AB = 10 ft.

So, the area of the rectangle ABCD is given by

$a_r=AD\times AB=36\times10=360~\textup{sq. ft}.$

Now, the base of each right-angled triangle is 9 ft and altitude is 12 ft.

So, the total area of both the right-angled triangle will be

$a_t=2\times\dfrac{1}{2}\times 9\times12=108~\textup{sq. ft}.$

Therefore, the total surface area of the given right triangular prism is given by

$A_s=a_r+a_t=360+108=468~\textup{sq ft}.$

Thus, the surface area of the given right-triangular prism is 468 sq. ft.

Option (C) is CORRECT.