Surface Area• What does it mean to you?• Does it have anything to do with what is in

the inside of the prism.?• Surface area is found by finding the area of

all the sides and then adding those answers up.

• How will the answer be labeled?• Units2 because it is area!

Rectangular Prism

How many faces are on here? 6

Find the area of each of the faces.

A

B

C

4

5 in

6Do any of the faces have the same area? A = 5 x 4 = 20 x 2 =40

B = 6 x 5 = 30 x 2 = 60

C = 4 x 6 = 24 x 2 = 48

If so, which ones?

148 in2

Opposite faces are the same.

Find the SA

CubeAre all the faces the same? YES

4m How many faces are there? 6

Find the Surface area of one of the faces.

A

4 x 4 = 16 Take that times the number of faces.X 6

96 m2SA for a cube.

Triangular PrismHow many faces are there? 5

How many of each shape does it take to make this prism?

2 triangles and 3 rectangles = SA of a triangular prism

4

3

5

10 m

Find the surface area. Start by finding the area of the triangle.

4 x 3/2 = 6

How many triangles were there? 2

x 2= 12

Find the area of the 3 rectangles.

5 x 10 = 50 = front

4 x 10 = 40 = back

3 x 10 = 30 = bottom

SA = 132 m2What is the final SA?

SA

• You can find the SA of any prism by using the basic formula for SA which is

• 2B + LSA= SA• LSA= lateral Surface area• LSA= perimeter of the base x height of the

prism• B = the base of the prism.

Triangular Prisms• Use the same triangular prism we used before.

Let’s us the formula this time. 2B + LSA=SA• Find the area of the base, which is a triangle

because it is a triangular prism. You will need two of them.

• Now, find the perimeter of that same base and multiply it by how many layer of triangles are in the picture. That is the LSA.

• Add that to the two bases. Now you should have the same answer as before.

• Either way is the correct way.

Cylinders6 10m

What does it take to make this?

2 circles and 1 rectangle= a cylinder

2 B 3.14 x 9 = 28.26 X 2 = 56.52

+ LSA(p x H) 3.14 x 6 =18.84 x 10 = 188.4

SA = 244.92

2B + LSA = SA

Why should you learn about surface area?Is it something that you will ever use in

everyday life?If so, who do you know that uses it?Have you ever had to use it outside of

math?

Surface Areas of Pyramids

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.

Heighth

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 Perime

ter

Slant Height

BLS Surface Area

Lateral 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

#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

Surface Area of a Cone

With slides from www.cohs.com/.../229_9.3%20Surface%20Area%20of%20Pyramids%20and%20Cones%20C...

• A cone has a circular base and a vertex that is not in the same plane as a base.

• In a right cone, the height meets the base at its center.

• The height of a cone is the perpendicular distance between the vertex and the base.

• The slant height of a cone is the distance between the vertex and a point on the base edge.

Height

Lateral Surface

The vertex is directly above the center of the circle.

Baser

Slant Height

r

Surface Area of a Cone• Surface Area = area of base + area of sector

= area of base + π(radius of base)(slant height)

S B r 2r r

2B r r

Lateral Area of a Cone

• Since Lateral Area = Surface Area – area of the base

2r r L.A. =

Example 1:• Find the surface area of the cone to the nearest

whole number.

a. r = 4 slant height = 64 in.

6 in.

2S r r 2(4) (4)(6)

16 24 4040(3.14)

2126 .in

Example 2:• Find the surface area of the cone to the nearest whole

number.

b.

First, find the slant height. Next, r = 12,

12 ft.

5 ft.

2 2 2r h 2 2(12) (5)

144 25 169 169 13

13.2S r r

2(12) (12)(13) 144 156 300

2942 .ft

On your own #1

Calculate the surface area of:

• S = (7)2 + (7)(11.40)

• S = 49 + 79.80• S = 128.8

2S r r

On your own #2Calculate the lateral area of:

• L.A. = (5)(13)

• L.A. = 65

2S r r L.A. =