10.2 Surface Areas of
Pyramids and Cones
1. For a pyramid that is not regular, there is no simple
formula for its lateral area. Look at the figures below.
Because the lateral faces are not congruent, you must
calculate each of the four areas and add them up.
If the pyramid or cone is REGULAR, there
is a simple LATERAL AREA formula to use.
LA =
= slant perimeter
height (circumference)
of base
If the slant height is 10mm, and each base
edge was 4mm, what is the lateral area?
LA =
4. The surface area of any pyramid or
cone is the SUM of its LATERAL FACE(S)
and the AREA of its BASE.
SA = L.A.+ B
Lateral Area
Base Area
6. A right cone has a slant height of 12
and a radius of 6. Find the lateral area.
LA =
l = 12
p = 2πr
7. A right square pyramid has a slant height
of 5 and a height of 4. Find the surface area.
SA = L.A.+ B
8. Find the lateral and surface areas of the regular pyramid shown.
LA =
SA = L.A.+ B
9. How much paper would be needed to construct a
birthday hat which is in the shape of a right cone with
a radius of 3.2 inches and a slant height of 5 inches?
What formula would you use?
Lateral Area or Surface Area?
10. Review: A gift box measures 40in. by 28in. by 12in.
Can the box be completely covered by a 30‐ft2 roll of
wrapping paper? Why or why not?
SA = LA + 2B
= perimeter x height + 2B