What is the missing length l of the triangular prism if the surface area is 524 square centimeters?(1 point)Responses16 cm16 cm10 cm10 cm17 cm17 cm8 cm
there is 10 and 10 6 and 8 so what is l
The missing length l of the triangular prism can be calculated by finding the dimensions of the triangular bases of the prism.
Let's assume the base of the triangular prism is a right-angled triangle with the sides measuring 10 cm and 6 cm. The surface area of a triangular prism can be calculated as:
Surface Area = 2 * area of triangular base + perimeter of base * height
The area of a right-angled triangle is 0.5 * base * height, so:
Area of triangular base = 0.5 * 10 * 6 = 30 square cm
Given that the surface area is 524 square cm, and the perimeter of a right-angled triangle is the sum of its sides, the perimeter can be calculated as:
Perimeter of triangular base = 10 + 6 + sqrt(10^2 + 6^2) = 22 + sqrt(136) ≈ 34.71 cm
So, we substitute these values into the surface area formula to find l:
524 = 2 * 30 + 34.71 * l
524 = 60 + 34.71 * l
464 = 34.71 * l
l ≈ 13.35 cm
Therefore, the missing length l is approximately 13.35 cm.