Math help - Pythagorean theory

This is the problem:

The apothem of a right pyramid with a square base is 12cm. The side of the base is 10cm. Find the length of the congruent sides of the isosceles triangle.

An apothem in a regular pyramid is the slant height of one of its faces, each of which is an isoceles triangle. So, it's one of the short sides of a right triangle (half the face), the other being half the base length (in this case, 5cm). So you must have a 5-12-13 triangle, with 13cm being the length of the congruent sides of the triangular pyramid face. (5^2 + 12^2 = 13^2)

The apothem of a right pyramid bisects the base of a square pyramid and creates a right triangle at the bisector. Use the pythagorean theorem to find the side, s.

s^2 = 12^2 + (1/2(10))^2 = 144 + 5^2 = 144 + 25 = 169

take the square root of both sides.

s = sqrt(169)

s = 13.

12² + 5² = 169
√169 = 13
The congruent sides have length 13 cm.

http://www.flickr.com/photos/dwread/8176…

a2 plus b2 equals c2 so 12x12 plus 10x10 equals 244, then just do square root of 244.