How can we use rectangular pyramids?
There are two main calculations for a rectangular pyramid, surface area and volume.
To find the surface area of a pyramid, we can look at it in two ways.
- Surface area - using the net.
To find the surface area using the net, we are finding individual areas of the faces of the pyramid. In other words, you will find the area of the rectangle and separately find the area of the triangles. You will need to know the dimensions of the base as well as the height of each of the triangles.
2. Surface area - using the formula
If the base is a square, we can use the formula , where is the area of the base, is the perimeter of the base and is the slant height (the height of the triangles, not the pyramid. Note that this formula only applies for regular pyramids. This means the base has to be a regular shape, like a square.
The volume of a rectangular pyramid is exactly one-third the amount of it’s corresponding rectangular prism. To find the volume of a pyramid, we can use the following formula:
Where B is the area of the base and h is the height of the pyramid from the apex to the center of the base.
Sample Math Problems
Question
Find the surface area:
Solution
This is a rectangular pyramid, we need to find individual areas and add them up.
Area of the base: 6 x 12 = 72 square inches
Area of the triangle whose base is 6: ½ x 6 x 10 = 30 square inches
Area of the triangle whose base is 12: ½ x 12 x 8.5 = 51 square inches
Surface area = 72 + 2(30) + 2(51) = 234 square inches
Note that we are doubling the 30 and 51 because there are two triangles of equal areas.
Question
Find the surface area:
Solution
This is a square pyramid so we can find the surface area using the formula
