Bell WorkFind the surface area of each figure.

13 x 23 = 299 cm²

10 x 23 = 230 cm²

( ½ )(10)(12) = 60 cm²

Add them up!

SA = 299 + 299 + 230 + 60 +60

SA = 948 cm²

6 x 4 = 24 in²

3 x 4 = 12 in²

6 x 3= 18 in²

Add them up!

SA = 24 + 24 + 12 + 12+ 18 + 18

SA = 108 in²

Surface Area Continued

Definition• Surface Area – is the total number of square

units used to cover a 3-D surface.

Surface Area

• What does it mean to you?• Does it have anything to do with what is 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!

Shortcut for surface Area

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

SA= 2B + Ph• Ph = The surface area of all of the sides.– The sum of the surface areas of all of the faces

excluding the bases.• To find Ph: perimeter of the base x height of

the prism.• B = the area of the base of the prism.

Let’s start with a rectangular prism.

You can find the area for each surface and add them up, or surface area can be done using the formula.

SA = 2lw + 2lh + 2wh OR SA = 2B + Ph

Either method will give you the same answer.

Top/bottom 2(8)(4) = 64

Left/right 2(4)(7) = 56

Front/back 2(8)(7) = 112

Add them up!

SA = 232 cm²

Example:

7 cm

4 cm

8 cm

SA= 2B + Ph

B = (7)(4) = 28

P = 4 + 4 + 7 + 7 = 22

h = 8

SA= 2(28) + 22(8)

SA= 56 + 176

SA = 232 cm²

OR

Example:

8mm

9mm

6 mm 6mm

Find the AREA of each SURFACE

1. Top and bottom triangle:

A = 2(½ bh)

A =2( ½ )(6)(6)

A = 36

2. The two sides are the same.

A = 2lw

A = 2(6)(9)

A = 108

3. The back rectangle is different

A = lw

A = 8(9)

A = 72

4. ADD THEM ALL UP!

36+ 108+ 72

SA = 216 mm²

SA= 2B + Ph

SA= 2(18) + 20(9)

SA= 36 + 180

SA = 216 mm²

ORB = ( ½ )(6)(6) = 18

P = 6 + 6 + 8 = 20

h = 9

Cube

Are all the faces the same? YES

4m

How many faces are there? 6

Find the Surface area of one of the faces.

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

96 m2 SA for a cube.

Example

SA= 2B + Ph

SA= 2(16) + 20(15)

SA = 32 + 300

SA= 332 in²

B = 2 x 8 = 16 in²P = 2 + 2 + 8 +8 = 20 in

Find the Surface Area

Example

SA= 2B + Ph

SA= 2(184) + 50.4(21.5)

SA = 368 + 1,083.6

SA= 1,451.6 cm²

Perimeter of Base = (8.4)(6)P= 50.4 cm

Find the Surface Area

Example

CUBEArea of one face: 5² = 25

SA= (6)(25)

SA= 150 m²

Find the Surface Area

Example• The area of one base of a triangular prism is

18 square feet. The perimeter of the triangular base is 19 feet. The height of the prism is 21 feet. Find the surface area of the triangular prism.

21 ft

SA= 2B + Ph

SA= 2(18) + 19(21)

SA = 36 + 399

SA= 435 ft²

Example• How much wrapping paper do you need to

completely cover a rectangular box that is 20 inches by 18 inches by 6 inches?

SA= 2B + Ph

SA= 2(360) + 76(6)

SA= 720 + 456

SA= 1176 in²B = 20 x 18 = 360 in²

P = 20 + 20 + 18 + 18 = 76 in

Practice: Surface Area Worksheet

REMEMBER!

When in doubt….draw a net to find the surface area!