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.

Answer 1

To find the surface area of a triangular prism, we need to find the area of the two triangular bases and the three rectangular sides.

First, let's find the area of the triangular bases:
Area of a triangle = 0.5 * base * height
Area of base 1 = 0.5 * 17 * 9
Area of base 1 = 76.5 square inches

Area of base 2 = 0.5 * 12 * 9
Area of base 2 = 54 square inches

Next, let's find the area of the three rectangular sides:
Area of a rectangle = length * width
Area of side 1 = 17 * 10
Area of side 1 = 170 square inches

Area of side 2 = 10 * 10
Area of side 2 = 100 square inches

Area of side 3 = 12 * 10
Area of side 3 = 120 square inches

Now, let's calculate the total surface area by adding the areas of the bases and sides:
Total surface area = 2(base area) + 3(side area)
Total surface area = 2(76.5 + 54) + 3(170 + 100 + 120)
Total surface area = 2(130.5) + 3(390)
Total surface area = 261 + 1170
Total surface area = 1431 square inches

Therefore, the surface area of the display showcase is 1431 square inches.

Answer 2

wrong

Answer 3

I apologize for the mistake. Let's reevaluate the surface area calculation for the triangular prism display showcase.

The surface area of a triangular prism can be calculated using the formula:
Surface Area = 2 * base area of triangle + perimeter of base * height of prism

First, let's calculate the base area of the triangle:
Base area = 0.5 * base * height
Base area = 0.5 * 17 * 9
Base area = 76.5 square inches

Next, let's calculate the perimeter of the base:
Perimeter = s1 + s2 + s3
Perimeter = 10 + 12 + 17
Perimeter = 39 inches

Now, calculate the total surface area:
Surface Area = 2 * 76.5 + 39 * 9
Surface Area = 153 + 351
Surface Area = 504 square inches

Therefore, the correct surface area of the display showcase is 504 square inches.