# The side edge of a regular triangular pyramid is 10m, and the side of the base is 12m.

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.

Solution:

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 