Use the image to answer the question.%0D%0A%0D%0A%0D%0A%0D%0AFind the lateral surface area of the triangular pyramid with an equilateral base represented in the net.

Answer 1

To find the lateral surface area of the triangular pyramid, we need to find the area of each of the three triangular faces and add them together.

Each triangular face is an equilateral triangle with side length 5 cm. The formula to find the area of an equilateral triangle is:
Area = (sqrt(3)/4) * s^2

Plugging in the side length of 5 cm:
Area = (sqrt(3)/4) * 5^2 = (sqrt(3)/4) * 25 = (25sqrt(3))/4 ≈ 10.83 cm^2

Since there are three triangular faces, the total lateral surface area of the triangular pyramid is:
3 * 10.83 cm^2 = 32.49 cm^2

So, the lateral surface area of the triangular pyramid is approximately 32.49 square centimeters.