find the volume of a square pyramid. Round to the nearest tenth(slant height=20 base=13)

To find the volume of a square pyramid, you can use the formula:

Volume = (1/3) * base area * height

The base area is the area of the square base, which can be found by squaring the length of one side of the square. In this case, the base length is 13, so the base area is 13 * 13 = 169 square units.

The height of the pyramid can be calculated by using the Pythagorean theorem. The slant height, which is the distance from the apex (top) of the pyramid to a corner of the square base, is given as 20 units. Since the slant height is the hypotenuse of a right triangle, you can use the following formula:

Height = √(slant height^2 - (base length/2)^2)

Plugging in the given values, the height = √(20^2 - (13/2)^2)

Height = √(400 - 84.5) ≈ √315.5 ≈ 17.7 units

Now, substitute the values into the volume formula:

Volume = (1/3) * 169 * 17.7 ≈ 945.73 cubic units

So, the volume of the square pyramid, rounded to the nearest tenth, is approximately 945.7 cubic units.

V = 1/3b^2 * h

V = (1/3) * 169 * 20

V = 1,126.666 = 1.126.7