Question

The base of a triangular prism is 8 cm. The width of one of the rectangles is 10 cm. The prism length is x. The height of the base of the triangular prism is 6 cm. The surface area of the triangular is 524 square centimeters. What is the missing prism length??

Answer 1

To find the missing prism length, we first need to calculate the total surface area of the triangular prism. A triangular prism has 2 triangular bases and 3 rectangular faces.

The area of a triangle is 1/2 * base * height, so the area of one triangular base is 1/2 * 8 * 6 = 24 square cm. Since there are 2 triangular bases, the total area of the triangular bases is 2 * 24 = 48 square cm.

The area of a rectangle is length * width, so the area of each rectangular face is 8 * 10 = 80 square cm. Since there are 3 rectangular faces, the total area of the rectangular faces is 3 * 80 = 240 square cm.

Therefore, the total surface area of the triangular prism is 48 + 240 = 288 square cm.

We are given that the total surface area of the triangular prism is 524 square cm. Therefore, we can set up the equation:

288 + 2(8x) + 3(10x) = 524

288 + 16x + 30x = 524

46x = 236

x = 236/46

x ≈ 5.13 cm

Therefore, the missing prism length is approximately 5.13 cm.