A right pyramid has a square base with sides of length 10 units. Each segment connecting the apex
to a midpoint of a side of the base has length 13 units. What is the volume of the pyramid?
To find the volume of a pyramid, we use the formula:
Volume = (1/3) * base area * height
First, we need to find the height of the pyramid. We can do this by creating a right triangle with the side length from the apex to the midpoint of a side of the base as the hypotenuse, the height of the pyramid as one leg, and half of the side length of the base (5 units) as the other leg.
Using the Pythagorean theorem:
height^2 + 5^2 = 13^2
height^2 + 25 = 169
height^2 = 144
height = 12 units
Next, we need to find the area of the base, which is a square with sides of length 10 units:
Base area = 10 * 10 = 100 square units
Now we can calculate the volume of the pyramid:
Volume = (1/3) * 100 * 12 = 400 cubic units
Therefore, the volume of the pyramid is 400 cubic units.