Surface Area and Volume: Surface Area and Volume of Pyramids and Cones

Central Angles

To find the surface area of a pyramid, we will use the same steps we used for prisms.

Surface Area:

  1. Draw and label the surfaces of a figure.
  2. Find the area of each surfaces.
  3. Add the areas together.
  4. Label the answer with 'square units'.


Example:
Let’s find the surface area of the pyramid we first looked at.  Let’s say that the dimensions of the base are L = 5 ft and W = 5 ft, and the slant height of each side is l = 6 ft.

Pyramid with square base
Pyramid

 

1. Draw and label the surfaces of the figure.

Sides of the pyramid laid out flat
Sides of the pyramid

 

2. Find the area of each surfaces.

Square base: s·s = 5·5 = 25

Four triangular sides: one-half b h equals one-half times 5 times 6 equals 15 

3. Add the areas together.

SA = base + 4(sides) = 25 + 4(15) = 85

4. Label the answer with ‘square units’.

The total surface area is 85 ft².