To find the missing length l of the triangular prism, we first need to calculate the total surface area of the triangular prism using the given measurements.
The surface area of a triangular prism can be calculated using the formula:
Surface Area = 2*(base area of triangle) + (perimeter of base)*height
Given the measurements from the image:
First, we must find the base area of the triangle:
Base area of the triangle = (1/2) * base * height
Base area = (1/2) * 8 * 10
Base area = 40 square cm
Next, we calculate the perimeter of the base:
Perimeter of base = 8 + 8 + 10
Perimeter of base = 26 cm
Now, we calculate the total surface area of the triangular prism using the formula:
Total Surface Area = 2 * base area of triangle + perimeter of base * height
Total Surface Area = 2 * 40 + 26 * l
Total Surface Area = 80 + 26l
Given that the total surface area is 524 sq cm:
80 + 26l = 524
26l = 444
l = 444 / 26
l = 17 cm
Therefore, the missing length l of the triangular prism is 17 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 8 cm 8 cm 10 cm 10 cm 17 cm 17 cm 16 cm
1 answer
1 answer