if the height of a regular triangular pyramid base equals 372, the base equals 6, and the slant height equals 8. What is the surface area?
To calculate the surface area of a triangular pyramid, we need to calculate the area of each triangular face and the area of the base and then sum them up.
First, let's calculate the area of one triangular face. We have the height of the pyramid (h = 372), the base length of the triangle (b = 6), and the slant height (l = 8).
The formula for the area of a triangle is A = (1/2) * base * height. Substituting the given values, we get A = (1/2) * 6 * 8.
A = 24.
Since a triangular pyramid has 4 triangular faces, the total area of the triangular faces is 4 * A = 4 * 24 = 96.
Now let's calculate the area of the base. The base of the pyramid is a regular triangle, which has three sides of equal length (6 in this case). The formula for the area of an equilateral triangle is A = (sqrt(3) / 4) * side^2. Substituting the given values, we get A = (sqrt(3) / 4) * 6^2.
A = 9 * sqrt(3).
Now we can calculate the total surface area. The surface area of the pyramid is the sum of the areas of the triangular faces and the base. Surface Area = 96 + 9 * sqrt(3).
Approximately, the surface area is 96 + 15.588 = 111.588 square units.