Question

using a net to find the surface area of a triangular prism

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

a = 12 yd
b = 13 yd
c = 4 yd
d = 5 yd

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

Explanation:

Step1: Calculate the area of the triangular bases

The formula for the area of a triangle is \(A_{triangle}=\frac{1}{2}\times base\times height\). Here, the base of the triangle is \(4\) yd and the height is \(5\) yd.
\(A_{triangle}=\frac{1}{2}\times4\times5 = 10\) square - yards. Since there are \(2\) triangular bases, \(A_{triangles}=2\times10 = 20\) square - yards.

Step2: Calculate the area of the rectangular faces

There are three rectangular faces.

• For the rectangle with sides \(4\) yd and \(12\) yd: \(A_1 = 4\times12=48\) square - yards.
• For the rectangle with sides \(5\) yd and \(12\) yd: \(A_2 = 5\times12 = 60\) square - yards.
• For the rectangle with sides \(13\) yd and \(12\) yd: \(A_3=13\times12 = 156\) square - yards.

Step3: Calculate the total surface area

The total surface area \(A\) of the triangular prism is the sum of the areas of the triangular bases and the rectangular faces.
\(A=A_{triangles}+A_1 + A_2+A_3\)
\(A = 20+48 + 60+156\)
\(A=284\) square - yards.

Answer:

The surface area of the triangular prism is \(284\) square - yards.