Surface Area of Pyramids

ADDITION TO DIAGRAM – NEW VOCAB

The slant height of a regular pyramid is the distance from the vertex to the midpoint of an edge of the base.

The lateral faces of a regular pyramid can be arranged to cover half of a rectangle with a height equal to the slant height of the pyramid. The width of the rectangle is equal to the base perimeter of the pyramid.

Example 1• Find the surface area of the regular

pyramid. n represents the number of sides of the base, and s represents the length of one side of the base, and l is the slant height.

n = 3, s = 14, l = 14

Example 2• Find the surface area of the regular

pyramid. n represents the number of sides of the base, and s represents the length of one side of the base, and l is the slant height.

n = 6, s = 5.2, l = 13

Example 3• Find the surface area of the regular

pyramid. n represents the number of sides of the base, and s represents the length of one side of the base, and l is the slant height.

n = 4, s = 12, l = 13

Example 4• Work backwards to solve for the

missing information.

In a rectangular pyramid, one side of the base is 30 in. The slant height of the pyramid is 29 in, and the SA = 4180 square inches. What is the length of

the other side of the rectangular base?

Example 5• Work backwards to solve for the

missing information.

In a triangular pyramid, the base area is 50 square mm. The slant height of the pyramid is 40 mm, and the SA = 250

square mm. What is the perimeter of the triangular base?

Example 6• Work backwards to solve for the

missing information.

In a square pyramid, the slant height is 5 cm, and the SA = 96 square cm. What is

the length of one side of the base?