To find the missing length l, we need to first find the surface area of the triangular prism.
The formula to find the surface area of a triangular prism is:
Surface Area = 2B + Ph
Where B is the area of the triangular base, P is the perimeter of the base, and h is the height of the prism.
In this case, the surface area is given as 524 square centimeters. The base of the triangular prism is a right triangle with one leg of 8 cm and the other leg of 15 cm (8 + 7 = 15).
The area of the triangular base B can be calculated as:
B = 0.5 * base * height = 0.5 * 8 * 15 = 60 square centimeters
The perimeter of the triangular base P can be calculated as:
P = a + b + c = 8 + 15 + 17 = 40 cm
The height h of the prism is the missing length l.
Now, plug in the values into the formula for the surface area:
524 = 2(60) + 40l
524 = 120 + 40l
404 = 40l
l = 404 / 40
l = 10.1 cm
Therefore, the missing length l of the triangular prism is approximately 10.1 cm. The closest option from the choices given is 10 cm.
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? (1 point) Responses 17 cm 17 cm 8 cm 8 cm 10 cm 10 cm 16 cm
1 answer