The volume of a pyramid is one-third the product of the area of the base and the height.
V=1/3 B h
Let's consider the given pyramid.
We know two sides of the base and we have been given a slant height. The given information is not sufficient to solve the problem. Therefore, we will also assume the pyramid has a base in the shape of a rectangle and that its height is in the center of the base.
Let's create a right triangle with the height as one of its sides and the slant height as the hypotenuse.
The right triangle has one side with a length of 3 meters and a hypotenuse with a length of 12 meters. By using the Pythagorean Theorem we can find the pyramid's height, h.
The height of a pyramid must be non-negative, which is why we only kept the principal root when solving the equation. Next we will use the formula for area of a rectangle to find the area of the base, B.
B=l w
⇓
B=10(6)= 60
We can now calculate the volume of the pyramid.
V=1/3 B h
⇓
V=1/3( 60)( sqrt(135) ) ≈ 232.4
The volume of the pyramid to the nearest tenth is 232.4 m^3.
