Question

lengths are in yards.)
(a) find the following side lengths for the net.
a = 2 yd
b = 17 yd
c = 8 yd
d = 15 yd
(b) use the net to find the surface area of the prism.

Explanation:

Step1: Calculate the area of the triangular faces

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). For the given right - angled triangle with \(b = 15\) yd and \(h=8\) yd, the area of one triangular face is \(\frac{1}{2}\times15\times8=60\) square yards. Since there are 2 triangular faces, the total area of the triangular faces is \(2\times60 = 120\) square yards.

Step2: Calculate the area of the rectangular faces

There are three rectangular faces.

• For the rectangle with dimensions \(A = 2\) yd and \(B = 17\) yd, the area is \(A_1=2\times17 = 34\) square yards.
• For the rectangle with dimensions \(A = 2\) yd and \(C = 8\) yd, the area is \(A_2=2\times8=16\) square yards.
• For the rectangle with dimensions \(A = 2\) yd and \(D = 15\) yd, the area is \(A_3=2\times15 = 30\) square yards.

The total area of the rectangular faces is \(A_{rect}=34 + 16+30=80\) square yards.

Step3: Calculate the total surface area

The total surface area \(S\) of the prism is the sum of the area of the triangular faces and the area of the rectangular faces. So \(S=120 + 80=200\) square yards.

Answer:

The surface area of the prism is \(200\) square yards.