Surface Area of a Pyramid

The lateral surface area of a regular pyramid is the sum of the areas of its lateral faces.

The total surface area of a regular pyramid is the sum of the areas of its lateral faces and its base.

The general formula for the lateral surface area of a regular pyramid is L.S.A.= 1 2 pl where p represents the perimeter of the base and l the slant height.

Example 1:

Find the lateral surface area of a regular pyramid with a triangular base if each edge of the base measures 8 inches and the slant height is 5 inches.

The perimeter of the base is the sum of the sides.

p=3(8)=24inches

L.S.A.= 1 2 (24)(5)=60 inches 2

The general formula for the total surface area of a regular pyramid is T.S.A.= 1 2 pl+B where p represents the perimeter of the base, l the slant height and B the area of the base.

Example 2:

Find the total surface area of a regular pyramid with a square base if each edge of the base measures 16 inches, the slant height of a side is 17 inches and the altitude is 15 inches.

The perimeter of the base is 4s since it is a square.

p=4(16)=64inches

The area of the base is s 2 .

B= 16 2 =256 inches 2

T.S.A.= 1 2 (64)(17)+256 =544+256 =800 inches 2

There is no formula for a surface area of a non-regular pyramid since slant height is not defined.  To find the area, find the area of each face and the area of the base and add them.