GEOMETRY: Chapter 12
12.3 Surface Area of Pyramids
and Cones
A pyramid is a polyhedron in which the base is a
polygon and the lateral faces are triangles with a
common vertex, called the vertex of the pyramid.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 810.
The intersection of two lateral faces is a
lateral edge. The intersection of the base
and a lateral face is a base edge. The
height of the pyramid is the
perpendicular distance between the base
and the vertex.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 810.
A regular pyramid has a regular polygon for a
base, and the segment joining the vertex and
the center of the base is perpendicular to the
base.
The lateral faces of a regular pyramid are
congruent isosceles triangles. The slant
height of a regular pyramid is the height
of a lateral face of the regular pyramid.
Ex. 1
A regular square pyramid has a height of 12 ft
and a base edge length of 10 ft. Find the area
of each lateral face of the pyramid.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 811.
Ex. 1
A regular square pyramid has a height of 12 ft
and a base edge length of 10 ft. Find the area
of each lateral face of the pyramid.
Answer: 65 ft2
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 811.
Theorem 12.4: Surface Area of a Regular Pyramid
The surface area S of a regular pyramid is
S= B + ½ Pl,
where B is the area of the base, P is the
perimeter of the bae, and l is the slant height.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 811.
Ex. 2.
Find the surface area of a regular octagonal
pyramid if the slant height is 18 ft. the
apothem of the base is 15.7 ft, and the sides
of the base are 13 ft.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 811.
Ex. 2.
Find the surface area of a regular octagonal
pyramid if the slant height is 18 ft. the
apothem of the base is 15.7 ft, and the sides
of the base are 13 ft.
Answer: 1752.4 ft2
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 811.
A cone has a circular base and vertex that is not in the
same plane as the base. The radius of the base is the
radius of the cone. The height is the perpendicular
distance between the vertex and the base.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 812.
In a right cone, the segment joining the vertex and the
center of the base is perpendicular to the base, and
the slant height is the distance between the vertex
and a point on the base edge.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 812.
Theorem 12.5: Surface Area of Right Cone
The surface area of a right cone is
Where B is the area of the base, C is the
circumference of the base, r is the radius of
the base, and l is the slant height.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 812.
Ex. 3
What is the surface area of the right cone?
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 812.
Ex. 3
What is the surface area of the right cone?
Answer: 360 (pi) cm2
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 812.
Ex. 4
A carpenter uses a weight in the shape of a
right cone to identify vertical lines. The cone
has a radius of 6.5 mm and a height of 13
mm. Find the approximate lateral area of the
weight.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 813.
Ex. 4
A carpenter uses a weight in the shape of a
right cone to identify vertical lines. The cone
has a radius of 6.5 mm and a height of 13
mm. Find the approximate lateral area of the
weight.
Answer: 297 mm2
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 813.
12.3, p. 814, #3-13 all, 15-23 odds
(16 questions)