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.
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
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1 answer