Answer:
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.=12pl 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)=24 inches
L.S.A.=12(24)(5)=60 inches2
The general formula for the total surface area of a regular pyramid is T.S.A.=12pl+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)=64 inches
The area of the base is s2 .
B=162=256 inches2
T.S.A.=12(64)(17)+256 =544+256 =800 inches2
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.
