Question

lengths are in feet.)
(a) find the following side lengths for the net.
a = 6 ft
b = 5 ft
c = 4 ft
d = 3 ft
(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 \(A=\frac{1}{2}bh\). For the right - angled triangle with \(b = 3\) ft and \(h = 4\) ft, \(A_{triangle}=\frac{1}{2}\times3\times4=6\) square feet. Since there are 2 triangular bases, \(A_{triangles}=2\times6 = 12\) square feet.

Step2: Calculate the area of the rectangular faces

There are three rectangular faces.

• For the rectangle with dimensions \(3\times6\): \(A_{1}=3\times6 = 18\) square feet.
• For the rectangle with dimensions \(4\times6\): \(A_{2}=4\times6=24\) square feet.
• For the rectangle with dimensions \(5\times6\): \(A_{3}=5\times6 = 30\) square feet.

The sum of the areas of the rectangular faces is \(A_{rectangles}=18 + 24+30=72\) square feet.

Step3: Calculate the total surface area

The total surface area \(A\) of the prism is the sum of the areas of the triangular bases and the rectangular faces. So \(A=A_{triangles}+A_{rectangles}\). Substitute the values: \(A = 12+72=84\) square feet.

Answer:

The surface area of the prism is \(84\) square feet.