Question

(a) find the following side lengths for the net.

a = 8 ft

b = 3 ft

c = 6 ft

d = 10 ft

(b) use the net to find the surface area of the prism.

ft²

Explanation:

Step1: Calculate the area of the two triangular faces

The formula for the area of a right - triangle is \(A_{\triangle}=\frac{1}{2}\times base\times height\). Here, the base is \(6\) ft and the height is \(8\) ft.
\(A_{triangles}=2\times\frac{1}{2}\times6\times8 = 48\)

Step2: Calculate the area of the three rectangular faces

There are three rectangles.

• One rectangle has dimensions \(6\times3\), its area \(A_1 = 6\times3=18\)
• One rectangle has dimensions \(8\times3\), its area \(A_2=8\times3 = 24\)
• One rectangle has dimensions \(10\times3\), its area \(A_3=10\times3=30\)

The sum of the areas of the rectangles \(A_{rectangles}=18 + 24+30=72\)

Step3: Calculate the total surface area

The total surface area \(A\) of the prism is the sum of the areas of the triangular faces and the rectangular faces.
\(A=A_{triangles}+A_{rectangles}\)
\(A = 48+72\)

Answer:

\(120\)