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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
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

Perimeter & Area of Rectangles & Parallelograms

6.1

Pre-Algebra

vocabulary
Vocabulary

perimeter

area

slide5

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.

example finding the perimeter of rectangles and parallelograms

5

14

Example: Finding the Perimeter of Rectangles and Parallelograms

A. Find the perimeter of the figure.

Add all side lengths.

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

slide7

Helpful Hint

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.

example finding the perimeter of rectangles and parallelograms1

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
Try This

A. Find the perimeter of the figure.

6

11

Add all side lengths.

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 this1
Try This

B. Find the perimeter of the figure.

5

13

P = 5 + 5 + 13 + 13

Add all side lengths.

= 36 units

slide11

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.

slide12

units2

units2

example using a graph to find area
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

slide14

Helpful Hint

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 area1
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

try this2

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

try this3

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
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
Example Continued

6

6

3

3

6

5

5

A = 6 • 5 + 6 • 2 + 6 • 5

Add the areas together.

= 30 + 12 + 30

= 72 units2

try this4
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

try this5

2

4

7

2

6

2

2

2

Try This

2

Find the area of the figure.

4

6

7

Add the areas together.

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
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
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
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
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