The base of the pyramid, a rectangle with sides 6 and 8 cm. The height of the pyramid is 12 cm.

The base of the pyramid, a rectangle with sides 6 and 8 cm. The height of the pyramid is 12 cm. It falls to the center of the base. Find the side edge.

Given:

a = 6 centimeters, b = 8 centimeters – the sides of the rectangle that is the base of the pyramid;

h = 12 centimeters – the height of the pyramid that falls to the center of the base.

It is required to find l (centimeter) – the length of the side edge of the pyramid.

Since there is a rectangle at the base of the pyramid, we determine the length of its diagonal:

c = (a ^ 2 + b ^ 2) ^ 0.5 = (6 ^ 2 + 8 ^ 2) ^ 0.5 = (36 + 64) ^ 0.5 = 100 ^ 0.5 = 10 centimeters.

That is, half of the diagonal will be equal to d = s / 2 = 10/2 = 5 centimeters.

Then, by the Pythagorean theorem, the length of the side edge will be equal to:

l = (d ^ 2 + h ^ 2) ^ 0.5 = (5 ^ 2 + 12 ^ 2) ^ 0.5 = (25 + 144) ^ 0.5 = 169 ^ 0.5 = 13 centimeters.

Answer: the side edge of the pyramid is 13 centimeters.