Surface Area of Pyramids and Cones.
Goal, to find the surface area of
pyramids and cones like those below.
In your own words; What is a pyramid?
A pyramid is a polyhedron in which has a base, that is
a polygon, and lateral faces which are triangles.
vertex
height
The height of a pyramid
is the perpendicular
distance from the
vertex to its base.
base
The height of a pyramid is the perpendicular
distance from the vertex to its base.
vertex
height
The slant height of a pyramid,
l
represented by , is the height
of any of its lateral faces.
base
Surface area of a pyramid (write this down)
Words; Surface area =
(base area) + ½ (base perimeter) ( slant height).
Symbols; S = B + ½ P
l
+
l
Surface area of a pyramid, a second method
(write this down)
1. Find the area of the base.
2. Find the area of one of the lateral sides.
3. Multiply the area of the lateral sides by the
number of sides.
4. Add the area of the base and the area found
in step 3.
A cone has a circular base and a vertex that is not in the
same plane as the base
vertex
slant
height
height
The height of a cone
is the perpendicular
distance between the
vertex and the base
base
r
The slant height
of a cone is the
distance between
the vertex and a
point on the base
edge.
Surface area of a cone (write this down)
Words; Surface Area = (base area)
+
(base radius) (slant height)
Symbols; S = B +
r
r
or S =
r2 +
r
+
r