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 answer

To find the surface area of the triangular prism showcase, we need to calculate the areas of the three rectangular faces and two triangular faces.

The formula for the surface area of a triangular prism is:
2 * (base area) + (lateral area)

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

Next, we calculate the lateral area:
Lateral area = perimeter of base * height
Perimeter of base = s1 + s2 + s3
Perimeter of base = 10 + 12 + 17
Perimeter of base = 39 inches

Lateral area = 39 * 10
Lateral area = 390 square inches

Now we can find the total surface area:
Surface area = 2 * base area + lateral area
Surface area = 2 * 76.5 + 390
Surface area = 153 + 390
Surface area = 543 square inches

Therefore, the surface area of Christian's model car and plane showcase is 543 square inches.