Question

use the net for the triangular prism to find the surface area. 15 ft 8 ft 8 ft 6 ft 10 ft

Explanation:

Step1: Calculate the area of the triangles

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). Here, \(b = 6\) ft and \(h = 8\) ft.
\(A_{triangle}=\frac{1}{2}\times6\times8= 24\) square feet. Since there are 2 triangles, \(A_{total - triangles}=2\times24 = 48\) square feet.

Step2: Calculate the area of the rectangles

There are three rectangles.

• For the rectangle with dimensions \(15\times10\): \(A_1=15\times10 = 150\) square feet.
• For the rectangle with dimensions \(15\times6\): \(A_2=15\times6=90\) square feet.
• For the rectangle with dimensions \(15\times8\): \(A_3=15\times8 = 120\) square feet.

\(A_{total - rectangles}=150 + 90+120=360\) square feet.

Step3: Calculate the total surface area

The surface area \(A\) of the triangular prism is the sum of the areas of the triangles and rectangles.
\(A=A_{total - triangles}+A_{total - rectangles}\)
\(A = 48+360\)

Answer:

\(408\) square feet