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, \(b = 8\) ft and \(h=6\) ft.
\(A_{triangle}=\frac{1}{2}\times8\times6 = 24\) \(ft^{2}\). Since there are 2 triangles, \(A_{triangles - total}=2\times24 = 48\) \(ft^{2}\)

Step2: Calculate the area of the rectangles

There are three rectangles.

• For the rectangle with dimensions \(15\times8\): \(A_{1}=15\times8=120\) \(ft^{2}\)
• For the rectangle with dimensions \(15\times6\): \(A_{2}=15\times6 = 90\) \(ft^{2}\)
• For the rectangle with dimensions \(15\times10\): \(A_{3}=15\times10=150\) \(ft^{2}\)

The total area of the rectangles is \(A_{rectangles - total}=120 + 90+150=360\) \(ft^{2}\)

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.
\(A=A_{triangles - total}+A_{rectangles - total}\)
\(A = 48+360\)

Answer:

\(408\) \(ft^{2}\)