1

Finding Surface Area

Step 1: Flatten the 3-D figure

A rectangular prism will flatten to 6 rectangles.

Depending on the dimensions of the 3-D figure, you will have different size rectangles.

Rectangular Prism

2

Finding Surface AreaStep 2: Transfer the dimensions to the 3-D figure

Dimensions: Length – 12 (left to right) Height – 8 (top to bottom) Width – 4 (front to back)

Rectangular Prism

Height 8

Length12

Width4

3

Finding Surface Area

Step 3: Transfer the dimensions from the 3-D figure to the flattened figure

Dimensions: Length – 12 (the longest side) Height – 8 (top to bottom) Width – 4 (front to back)

Rectangular Prism

Height 8

Length12

Width4

8

88

12

12

12

4

4

4

4

4

Finding Surface AreaStep 4: Find the AREA for each rectangle. (Length X Width)

Rectangular Prism

Height 8

Length12

Width 4

8

8 8

12

12

12

4

4

4

4

12 x 4

12 x 8

12 x 4

12 x 88 x 4 8 x 4

48 sq units

96 sq units

48 sq units

96 sq units32 32

5

Finding Surface AreaStep 4: Find the TOTAL SURFACE AREA for the 3-D Figure

Add together the areas for each rectangle

Rectangular Prism

8

124

48 sq units

96 sq units

48 sq units

96 sq units32 32

4848

9696

3232

= 352 sq. unitsTotal surface area

6

You can also use a table, instead of drawing the net.

8

12

4

Since opposite faces are congruent,you have three pairs of congruent rectangles.

Face Formula: A = bh

Area

Top 4 x 12 48

Bottom 4 x 12 48

Left 8 x 4 32

Right 8 x 4 32

Front 8 x 12 96

Back 8 x 12 96Total: 352 sq units

7

Group Practice:Fill out this table on your scratch paper to find the area for this figure.

Face Formula: A = bh

Area

Top

Bottom

Left

Right

Front

Back

Total: _____ sq units

8

CPS Practice:

The top and bottom faces each have an area of:

A) 64•224B)56C)None of the above

(Fill out a table for this figure as you do each of the next few questions.)

9

The left and right faces each have an area of:

A) 64•224B)56C)None of the above

10

The front and back faces each have an area of:

A) 64•224B)56C)None of the above

11

The total surface area of this rectangular prism is:

A) 765B) 896C) 344D) 688

12

Cube or SquareA cube or square will flatten to 6 equal squares.

13

Triangular Prism

A triangular prism will flatten to 3 rectangles and two equal triangles.

Step 1: Flatten the 3-D figure

14

Triangular Prism

8

6

8

6

15

15

15

Step 2: Transfer the dimensions to the 3-D Figure

Dimensions:

Base = 8

Height of Tri. = 6

Hypotenuse = 10

Height of prism = 15

1010

15

Triangular Prism

8

6

108

10

4

15

15

15

15

15

15

15

8

6

10

Transfer dimensions to Flattened Figure

Step 3:

6

8

16

Triangular Prism

8

6

108

10

6

15

15

15

15

15

15

15

8

6

10Find the area for each rectangle and triangle

Step 4:

8

6Step 5:

Write the area inside the specific shape

A = 8 x 15

A = 10 x 15

A = 6 x 15

120

150

90

A = 6 x 8

2 24 24

17

Triangular Prism

8

6

108

10

6

15

15

15

15

15

15

15

8

6

10Add all the areas for the total surface area

Step 6:

8

6

120

150

90

24 24

90

120150

2424

408 =Total surface

area

18

8

6

8

6

15

15

Try using a table instead of drawing a net.

Face A = ½(bh) Area

Triangle ½ (8 x 6) 24

Triangle ½(8 x 6) 24

Rectangle 1 8 x 15 120

Rectangle 2 6 x 15 90

Rectangle 3 10 x 15 150

Total: 408 sq units

19

CPS Practice

(Fill out a table for this figure as you do each of the next few questions.)

What is the area of each of the two triangles?

•48 m²A)48 m³B)96 m²C)96 m³

20

The three rectangles have the following areas:

•150, 150, 150A)150, 100, 100B)150, 150, 180C)180, 180, 150

21

The total surface area of this triangular prism is:

•600A)576B)480C)The same as the surface area of the moon.

22

Cylinder

A Cylinder will flatten to a rectangle and two equal circles.

Step 1: Flatten the 3-D shape

23

Cylinder Step 2: Transfer the dimensions to the 3-D shape

Height - 15Diameter - 8

Formulas to use: A =

15

Height

Diameter8

r = d 2

Height15

r = 4

Diameter = 8

2Π4 = 8Π

25

radius4

Step 3: Transfer dimensions to the flattened shape

8Π = 25

Length =

15

24

Cylinder Step 4: Find the area for each shape

25

15

8

15

8

4

3.14 x 4 x 4 = 50A = 50

A = 50

A = 375

25 x 15

Step 5: Add the areas for the shapes

5050

375

425 = Total surface area

25

Or, try using a table.

15

8 Face A =πr2 orA = Ch

Area

Circle π4² 50.25

Circle π4² 50.25

Rectangle 8π x 15 376.8

Total: 477.3 sq units

Just remember that the circumference of the circle is always one side of the rectangle and the height of the cylinder is the other.

26

CPS Practice

25

5

What is the approximate area of each of the circles in this cylinder?

•About 15 sq unitsA)About 30 sq unitsB)About 100 unitsC)About 75 sq units

27

25

5

How do you find the area of the lateral rectangle for this cylinder?

•Multiply the circumference of the circle by the height of the cylinder.A)Multiply the diameter of the circle by the height.B)Multiply the radius by the height.C)Multiply any two numbers that you happen to see on the diagram.

28

25

5What is the approximate area of the lateral rectangle?

•125 sq unitsA)About 750 sq unitsB)About 75 sq unitsC)About 1,200 sq units

29

25

5

The total surface area is about:

•750 sq unitsA)825 sq unitsB)900 sq unitsC)The same as a can of Spaghettio’s.