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?