To find the surface area of a triangular prism, we need to calculate the area of each face and then add them together.
1. The area of the base triangle:
The base of the triangular prism is a triangle with base b = 17 inches and height h = 9 inches. The formula for the area of a triangle is A = (1/2) * base * height. Plugging in the values:
A = (1/2) * 17 * 9
A = 76.5 inches^2
2. The area of the three rectangular faces:
The three rectangular faces are the three sides of the prism.
Face 1 (with side length s1 = 10 inches)
Area = l * s1 = 10 * 10 = 100 inches^2
Face 2 (with side length s2 = 12 inches)
Area = l * s2 = 10 * 12 = 120 inches^2
Face 3 (with side length s3 = 17 inches)
Area = l * s3 = 10 * 17 = 170 inches^2
3. Now, we add all the areas together:
Total surface area = Base area + 3 rectangle areas
Total surface area = 76.5 + 100 + 120 + 170
Total surface area = 466.5 inches^2
Therefore, the surface area of the display showcase is 466.5 square inches.
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.
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