Find the apothem of a regular triangular pyramid if the lateral edge is 13 cm and the base length is 10 cm.

1. By definition, in a regular triangular pyramid, all side faces are isosceles triangles.

2. Apothem is the height of the side face.

And the height in an isosceles triangle is also the median, by definition.

We calculate then what will be equal to half of the side of the triangle, which is the base:

10: 2 = 5.

Since we know, based on the task, that the edge of the pyramid is 13 cm, then we write down the equation and find the apothem (leg):

k ^ 2 + 5 ^ 2 = 13 ^ 2;

k ^ 2 = 144;

k1 = 12;

k2 = -12.

Answer: 12 cm.