What is the missing length l of the triangular prism if the surface area is 524 square centimeters?
A. 17 cm
B. 16 cm
C. 8 cm
D. 10 cm
We need to first determine the surface area of each face of the triangular prism.
The formula for the surface area of a triangular prism is:
Surface Area = 2*(base area) + (perimeter of base)* height
Given that the surface area is 524 square centimeters, and the base of the triangle has dimensions 15 cm by 10 cm, we can find the base area:
Base Area = (1/2)*base*height
Base Area = (1/2)*15*10
Base Area = 75 square cm
Now we can find the perimeter of the base:
Perimeter = 15 + 15 + 10 = 40 cm
Plugging these values into the formula for the surface area of a triangular prism, we get:
524 = 2*75 + 40*l
524 = 150 + 40l
374 = 40l
l = 9.35 cm
Since 9.35 cm is not one of the options given, we can round to the nearest whole number and choose the closest option:
Thus, the missing length l of the triangular prism is approximately 9 cm.
Answer: The closest option is C. 8 cm.