The triangular pyramid has a base of an equilateral triangle that is 15 cm on each side and is 13 cm across. The sides have a slant height of 17 cm. What is the surface area of this triangle pyramid?

Answer 1

To find the surface area of the triangular pyramid, we need to find the area of the base and the area of the three triangular faces.

1. Area of the base:
The area of an equilateral triangle can be calculated using the formula:
Area = (sqrt(3) / 4) * side^2
Area = (sqrt(3) / 4) * 15^2
Area = (sqrt(3) / 4) * 225
Area = (1.732 / 4) * 225
Area = 43.301 square cm

2. Area of the triangular faces:
To find the area of the triangular faces, we use the formula:
Area = (1/2) * base * height
The base of each triangular face is the side of the base triangle (15 cm), and the height is the slant height (17 cm).
Area = (1/2) * 15 * 17
Area = 127.5 square cm

Since there are three triangular faces, the total area of the triangular faces is:
Total area = 3 * 127.5
Total area = 382.5 square cm

3. Total surface area of the triangular pyramid:
Surface area = base area + total area of triangular faces
Surface area = 43.301 + 382.5
Surface area = 425.801 square cm

Therefore, the surface area of the triangular pyramid is 425.801 square cm.