if the height of a triangular pyramid base equals 9.3, the base equals 6, and the slant height equals 8. What is the surface area?
To find the surface area of a triangular pyramid, we need to find the areas of the four triangular faces and the area of the base.
First, let's find the area of each triangular face. We can use the formula for the area of a triangle: A = (1/2) * base * height.
1. Face 1: The base of this triangle is the slant height and the height is the height of the pyramid. So, the area of this face is (1/2) * 8 * 9.3 = 37.2.
2. Face 2: The base of this triangle is the slant height and the height is the height of the pyramid. So, the area of this face is also (1/2) * 8 * 9.3 = 37.2.
3. Face 3: The base of this triangle is the base of the pyramid and the height is the slant height. So, the area of this face is (1/2) * 6 * 8 = 24.
4. Face 4: The base of this triangle is the base of the pyramid and the height is the slant height. So, the area of this face is also (1/2) * 6 * 8 = 24.
Now, let's find the area of the base. The base of the pyramid is a triangle with a base of 6 and a height of 9.3. So, the area of the base is (1/2) * 6 * 9.3 = 27.9.
Finally, the total surface area of the pyramid is the sum of the areas of the four triangular faces and the area of the base: 37.2 + 37.2 + 24 + 24 + 27.9 = 150.3 square units.
Therefore, the surface area of the triangular pyramid is 150.3 square units.