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.
