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Perimeter & Area of Rectangles & Parallelograms. 6-1. Warm Up. Problem of the Day. Lesson Presentation. Pre-Algebra. Perimeter & Area of Rectangles & Parallelograms. 6-1. Pre-Algebra. Warm Up

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slide1

Perimeter & Area of Rectangles & Parallelograms

6-1

Warm Up

Problem of the Day

Lesson Presentation

Pre-Algebra

slide2

Perimeter & Area of Rectangles & Parallelograms

6-1

Pre-Algebra

  • 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

slide3

Problem of the Day

Six pennies are placed around a seventh so that there are no gaps. What figure is formed by connecting the centers of the six outer pennies?

regular hexagon

slide4

Learning Goal Assignment

Learn to find the perimeter and area of rectangles and parallelograms.

slide5

Vocabulary

perimeter

area

slide6

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.

slide7

5

14

Additional Example 1A: 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

slide8

Try This: Example 1A

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

slide9

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.

slide10

16

20

Additional Example 1B: Finding the Perimeter of Rectangles and Parallelograms

B. Find the perimeter of the figure.

P = 16 + 16 + 20 + 20

= 72 units

slide11

Try This: Example 1B

B. Find the perimeter of the figure.

5

13

P = 5 + 5 + 13 + 13

Add all side lengths.

= 36 units

slide12

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.

slide13

units2

units2

slide14

Additional Example 2A: 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

slide15

y

(–3, 3)

(1, 3)

x

5

4

(1, –2)

(–3, –2)

Try This: Example 2A

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

slide16

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.

slide17

Additional Example 2B: 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

slide18

y

(1, 3)

(5, 3)

x

4

(3, –1)

4

(–1, –1)

Try This: Example 2B

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

slide19

Additional Example 3: 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

slide20

Additional Example 3 Continued

6

6

3

3

6

5

5

A = 6 • 5 + 6 • 2 + 6 • 5

Add the areas together.

= 30 + 12 + 30

= 72 units2

slide21

Try This: Example 3

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

slide22

2

4

7

2

6

2

2

2

Try This: Example 3 Continued

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

+

+

+

slide23

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

slide24

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

slide25

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

slide26

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