Surface Areas of Surface Areas of PyramidsPyramids

Unit 5, Lesson 4Unit 5, Lesson 4

www.mrskimrocks.com/g10.4.ppt

Pyramids

Pyramid

Pyramid – A three dimensional figure in which one face, the base, is any polygon and the lateral faces are triangles that meet at a common vertex.

vertex

Pyramids cont.

The altitude of a pyramid is the perpendicular segment from the vertex to the plane of the base.

The length of the altitude is called the height.

Height

h

Pyramid

Pyramids cont.

Regular Pyramid – a pyramid whose base is a regular polygon.

Slant Height – the length of the altitude of the lateral face.

Slant Height

Pyramid

Formulas Lateral Area and Surface Area of a Regular Pyramid

PL2

1

Lateral Area

Base Perimeter

Slant Height

BLS Surface

AreaLateral Area

Base Area

B

Example 1: Finding Surface Area of a Pyramid Find the surface area of a square pyramid with base

edges 5 m and slant height 3 m.m 3

m 5

BLS

PL2

1

)5(4P

2530 S

20

)3(202

1L 2m 30

2sB 25B

2m 25B

2m 55S

#2 Finding Surface Area of a Pyramid Find the surface area of a regular hexagonal pyramid

with a slant height 20 in and sides 8 in.

BLS

pL2

1

)8(6P

3.166480 S

2in 48

)20(482

1L 2in 480

apB2

1

48342

1B

2in 396B

2in 3.646S

in 8

in 02

in 34

#3 Find the surface area of:

12 m

#4 Find the surface area of:

10”

15”

10”S = L + B

S = ½ (40)(15) + (10)(10)

S = 400 in2

Pyramids and Prisms

Pyramids and Cylinders