Use the image to answer the question. What is the missing length l of the triangular prism if the surface area is 524 square centimeters?
16 cm 16 cm
17 cm 17 cm
8 cm 8 cm
10 cm
To find the missing length, we first need to find the total surface area of the prism.
The formula for the surface area of a triangular prism is:
2* (base area) + (perimeter of base) * height
Given that the base is a triangle with two sides of 16 cm and one side of 17 cm, we can calculate the base area:
Base area = (1/2) * base * height
Base area = (1/2) * 16 * 17
Base area = 136 square cm
Perimeter of the base = 16 + 16 + 17 = 49 cm
Height = 10 cm
Now, plug in these values into the formula for surface area:
524 = 2 * 136 + 49 * 10
524 = 272 + 490
524 = 762
So, the missing length l is 10 cm.