Warm Up

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Warm Up. Graph the line segment for each set of ordered pairs. Then find the length of the line segment. 1. (–7, 0), (0, 0) 2. (0, 3), (0, 6) 3. (–4, –2), (1, –2) 4. (–5, 4), (–5, –2). 7 units. 3 units. 5 units. 6 units.

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Warm Up
• Graph the line segment for each set of ordered pairs. Then find the length of the line segment.
• 1. (–7, 0), (0, 0)
• 2. (0, 3), (0, 6)
• 3. (–4, –2), (1, –2)
• 4. (–5, 4), (–5, –2)

7 units

3 units

5 units

6 units

Perimeter & Area of Rectangles & Parallelograms

6.1

Pre-Algebra

Vocabulary

perimeter

area

Any side of a rectangle or parallelogram can be chosen as the base. The height is measured along a line perpendicular to the base.

Parallelogram

Rectangle

Height

Height

Side

Base

Base

Perimeter is the distance around the outside of a figure. To find the perimeter of a figure, add the lengths of all its sides.

5

14

Example: Finding the Perimeter of Rectangles and Parallelograms

A. Find the perimeter of the figure.

P = 14 + 14 + 5 + 5

= 38 units

Perimeter of rectangle.

or P = 2b + 2h

Substitute 14 for b and 5 for h.

= 2(14) + 2(5)

= 28 + 10 = 38 units

The formula for the perimeter of a rectangle can be written as P = 2b + 2h, where b is the length of the base and h is the height.

16

20

Example: Finding the Perimeter of Rectangles and Parallelograms

B. Find the perimeter of the figure.

P = 16 + 16 + 20 + 20

= 72 units

Try This

A. Find the perimeter of the figure.

6

11

P = 11 + 11 + 6 + 6

= 34 units

Perimeter of rectangle.

or P = 2b + 2h

Substitute 11 for b and 6 for h.

= 2(11) + 2(6)

= 22 + 12 = 34 units

Try This

B. Find the perimeter of the figure.

5

13

P = 5 + 5 + 13 + 13

= 36 units

Area is the number of square units in a figure. A parallelogram can be cut and the cut piece shifted to form a rectangle with the same base length and height as the original parallelogram. So a parallelogram has the same area as a rectangle with the same base length and height.

units2

units2

Example: Using a Graph to Find Area

Graph the figure with the given vertices. Then find the area of the figure.

A. (–1, –2), (2, –2), (2, 3), (–1, 3)

Area of a rectangle.

A = bh

Substitute 3 for b and 5 for h.

A = 3 • 5

A = 15 units2

The height of a parallelogram is not the length of its slanted side. The height of a figure is always perpendicular to the base.

Example: Using a Graph to Find Area

Graph the figure with the given vertices. Then find the area of the figure.

B. (0, 0), (5, 0), (6, 4), (1, 4)

Area of a parallelogram.

A = bh

Substitute 5 for b and 4 for h.

A = 5 • 4

A = 20 units2

y

(–3, 3)

(1, 3)

x

5

4

(1, –2)

(–3, –2)

Try This

Graph the figure with the given vertices. Then find the area of the figure.

A. (–3, –2), (1, –2), (1, 3), (–3, 3)

Area of a rectangle.

A = bh

Substitute 4 for b and 5 for h.

A = 4 • 5

A = 20 units2

y

(1, 3)

(5, 3)

x

4

(3, –1)

4

(–1, –1)

Try This

Graph the figure with the given vertices. Then find the area of the figure.

B. (–1, –1), (3, –1), (5, 3), (1, 3)

Area of a parallelogram.

A = bh

Substitute 4 for b and 4 for h.

A = 4 • 4

A = 16 units2

Example: Finding Area and Perimeter of a Composite Figure

Find the perimeter and area of the figure.

6

6

3

3

6

5

5

The length of the side that is not labeled is the same as the sum of the lengths of the sides opposite, 18 units.

P = 5 + 6 + 3 + 6 + 3 + 6 + 5 + 18

= 52 units

Example Continued

6

6

3

3

6

5

5

A = 6 • 5 + 6 • 2 + 6 • 5

= 30 + 12 + 30

= 72 units2

Try This

Find the perimeter of the figure.

The length of the side that is not labeled is 2.

2

4

6

7

7

2

6

2

P = 6 + 2 + 4 + 7 + 6 + 4 + 2 + 2 + 2 + 7

?

= 42 units

4

2

4

7

2

6

2

2

2

Try This

2

Find the area of the figure.

4

6

7

A = 2 • 6 + 7 • 2 + 2 • 2 + 4 • 2

7

2

6

2

= 12 + 14 + 4 + 8

2

2

= 38 units2

4

+

+

+

Lesson Quiz: Part 1

1. Find the perimeter of the figure.

12 ft

5 ft

5 ft

4 ft

5 ft

5 ft

44 ft

12 ft

Lesson Quiz: Part 2

2. Find the area of the figure.

12 ft

5 ft

5 ft

4 ft

5 ft

5 ft

108 ft2

12 ft

Lesson Quiz: Part 3

Graph the figure with the given vertices and find its area.

3. (–4, 2), (6, 2), (6, –3), (–4, –3)

50 units2

Lesson Quiz: Part 4

Graph the figure with the given vertices and find its area.

4. (4, –2), (–2, –2), (–3, 5), (3, 5)

42 units2