To find the surface area of a triangular pyramid, you need to find the areas of the triangular base and the three triangular faces.
The area of a triangle can be calculated using the formula:
Area = (1/2) * base * height
Given that the height of the triangular pyramid base is 6.5 and the base is 6, you can calculate the area of the triangular base as follows:
Base = 6
Height = 6.5
Area of triangular base = (1/2) * 6 * 6.5 = 19.5
To calculate the area of each triangular face, you can use the formula for the area of a triangle again, but this time you need to know the lengths of the sides.
Since you're given the slant height of the triangular pyramid as 8, you can use this value as one side of each triangular face. The other two sides are the height of the triangular pyramid base (6.5) and the base (6).
Face 1:
Base = 6
Height = 6.5
Slant height = 8
Area of triangular face 1 = (1/2) * 6 * 8 = 24
Face 2:
Base = 6
Height = 6.5
Slant height = 8
Area of triangular face 2 = (1/2) * 6 * 8 = 24
Face 3:
Base = 6
Height = 6.5
Slant height = 8
Area of triangular face 3 = (1/2) * 6 * 8 = 24
To find the total surface area, add up the areas of the base and the three faces:
Total Surface Area = Area of triangular base + Area of triangular face 1 + Area of triangular face 2 + Area of triangular face 3 = 19.5 + 24 + 24 + 24 = 91.5
Therefore, the surface area of the triangular pyramid is 91.5.
if the height of a triangular pyramid base equals 6.5, the base equals 6, and the slant height equals 8. What is the surface area?
1 answer
1 answer