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??

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.