Question

What is the surface area of a display case if it is the shape of a triangular prism with the following dimensions: height is 9 in, base is 17 in, s1 is 10 in, the S2 is 12 in, the S3 is 17 in, and the length is 10 in. Show the answer in inches squared

Answer 1

First, we need to calculate the surface area of each face of the triangular prism:

1. Base: The formula for the area of a triangle is A = 1/2 * base * height.
A = 1/2 * 17 in * 9 in = 76.5 sq in

2. S1: S1 = 10 in x 10 in = 100 sq in

3. S2: S2 = 12 in x 10 in = 120 sq in

4. S3: S3 = 17 in x 10 in = 170 sq in

Now, we will add up the surface areas of all the faces to find the total surface area of the triangular prism:

Total surface area = Base + 2(S1) + 2(S2) + 2(S3)
= 76.5 sq in + (2 * 100 sq in) + (2 * 120 sq in) + (2 * 170 sq in)
= 76.5 sq in + 200 sq in + 240 sq in + 340 sq in
= 856.5 sq in

Therefore, the surface area of the triangular prism display case is 856.5 square inches.