The side edge of a regular triangular pyramid is 10m, and the side of the base is 12m. Find the area of the side surface of the pyramid.
Given: 10m – side edge of the pyramid, 12m – side of the base.
Find: the area of the side surface of the pyramid.
Let’s call our pyramid – SABC, where S is the top of the pyramid
In order to find the area of the lateral surface of the pyramid, you need to find the area of all faces, except for the base. In the problem statement it is said that the pyramid is correct *, which means that all its side faces are equal. It is enough for us to find the area of one side face.
SAB – isosceles triangle, behind the sides SA = SB = 10m;
S (edges) – S (SAB);
S (SAB) = 1/2 * h * 12;
h is the height of the triangle;
If the triangle is isosceles, then its height is both the median and the bisector.
Then the height h divides the side of the base AB in half (12/2 = 6)
Find h, by the Pythagorean theorem:
h = √100-36 = 8m;
Find the area of the triangle (face):
S (edges) = 1/2 * 8 * 12 = 48m²
S (side surface) = 3 * 48 = 144m²
Correct answer: 144m²