Question

Question Christian collects model cars and planes. He has a display showcase of all of his collectors' items. Solve this real-world problem to find the surface area of the display showcase if it is the shape of a triangular prism with the following dimensions: h =9 inches, b =17 inches, s1 =10 inches, s2 =12 inches, s3 = 17 and l =10 inches.(1 point) S.A.= in.2

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the surface area of a triangular prism, we need to calculate the area of each of its faces and then add them all together.

The formula for the surface area of a triangular prism is:
S.A. = 2(base area) + (perimeter of base * height) + (sum of all three face areas)

First, we find the base area:
Base area = (1/2) * base * height
Base area = (1/2) * 17 * 9
Base area = 76.5 square inches

Next, we find the perimeter of the base:
Perimeter of base = s1 + s2 + s3
Perimeter of base = 10 + 12 + 17
Perimeter of base = 39 inches

Now we find the sum of the three face areas:
Face 1 area = base area
Face 1 area = 76.5 square inches

Face 2 area = base area
Face 2 area = 76.5 square inches

Face 3 area = (side length * height) / 2
Face 3 area = (17 * 10) / 2
Face 3 area = 85 square inches

Now we can plug all these values into the formula for surface area:
S.A. = 2(76.5) + (39 * 9) + (76.5 + 76.5 + 85)
S.A. = 153 + 351 + 238
S.A. = 742 square inches

Therefore, the surface area of the display showcase is 742 in².