if the height of a regular 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 regular triangular pyramid, we need to calculate the areas of the triangular base and the three triangular faces.
The area of the base can be found using the formula for the area of a triangle: A = (1/2) * base * height.
Given that the base of the triangle is 6 units and the height is 9.3 units, we can calculate the area of the base:
A_base = (1/2) * 6 * 9.3 = 27.9 square units.
Each triangular face of the pyramid is an isosceles triangle, where the base is the slant height and the two equal sides are the height of the pyramid. The area of an isosceles triangle can be found using the formula: A = (1/2) * base * height.
Given that the base (slant height) is 8 units and the height is 9.3 units, we can calculate the area of each triangular face:
A_face = (1/2) * 8 * 9.3 = 37.2 square units.
Since the regular triangular pyramid has four faces (including the base), the total surface area is obtained by adding the areas of all the faces:
Surface Area = 4 * A_face + A_base
= 4 * 37.2 + 27.9
= 148.8 + 27.9
= 176.7 square units.
Therefore, the surface area of the regular triangular pyramid is 176.7 square units.