Christian collects model cars in 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 equals 9 inches B equals 17 inches What equals 10 inches is two equals 12 inches three equals 17 inches and L equals 10 inches

Answer 1

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

First, let's find the area of the triangular faces:

1. Base of the triangle:
Area = (1/2) * base * height
Area = (1/2) * 17 * 9
Area = 76.5 square inches

2. Side 1 of the triangle:
Area = (1/2) * base * height
Area = (1/2) * 10 * 12
Area = 60 square inches

3. Side 2 of the triangle:
Area = (1/2) * base * height
Area = (1/2) * 12 * 17
Area = 102 square inches

Now, let's find the area of the rectangular faces:

1. Front face:
Area = length * height
Area = 10 * 9
Area = 90 square inches

2. Back face:
Area = length * height
Area = 10 * 9
Area = 90 square inches

Now, let's add up all the areas to find the total surface area of the triangular prism:

Total Surface Area = 2 * (Front face + Back face) + 2 * (Base of the triangle) + 2 * (Side of the triangle)
Total Surface Area = 2 * (90 + 90) + 2 * (76.5) + 2 * (60 + 102)
Total Surface Area = 180 + 153 + 324
Total Surface Area = 657 square inches

Therefore, the surface area of the display showcase is 657 square inches.