What is the missing length l of the triangular prism if the surface area is 524 square centimeters?

Question

17cm
8cm
16cm
10cm

Answer 1

To find the missing length of a triangular prism, we first need to know the formula for the surface area of a triangular prism.

The formula for the surface area of a triangular prism is:
Surface Area = 2*(Area of the base) + (Perimeter of the base)*l

Where l is the missing length we are trying to find.

Given that the surface area is 524 square centimeters, and the base is a right-angled triangle with sides 8cm and 17cm (using the Pythagorean theorem to find the hypotenuse), we can find the area of the base:

Area of the base = (1/2) * base * height
Area of the base = (1/2) * 8 * 15 = 60 square centimeters

Next, we need to find the perimeter of the base:

Perimeter of the base = sum of all three sides
Perimeter of the base = 8 + 17 + hypotenuse
Perimeter of the base = 8 + 17 + 15 = 40 cm

Now, we can plug the values into the formula for the surface area and solve for l:

524 = 2*(60) + (40)*l
524 = 120 + 40l
404 = 40l
l = 404/40
l = 10.1

Therefore, the missing length l of the triangular prism is 10.1 cm.