Pre-Algebra 6-1 Perimeter & Area of Rectangles & Parallelograms 6-1 Perimeter & Area of Rectangles & Parallelograms Pre-Algebra Warm Up Warm Up Problem

Pre-Algebra

6-1 Perimeter & Area of Rectangles & Parallelograms6-1 Perimeter & Area of Rectangles

& Parallelograms

Pre-Algebra

Warm Up

Problem of the Day

Lesson Presentation

Pre-Algebra

6-1 Perimeter & Area of Rectangles & Parallelograms

Warm UpGraph 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

Pre-Algebra


Pre-Algebra


Problem of the DaySix 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

Pre-Algebra


Learning Goal Assignment

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

Pre-Algebra


perimeter

area

Vocabulary

Pre-Algebra


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

Height HeightSide

Base Base

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

Rectangle Parallelogram

Pre-Algebra


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

A. Find the perimeter of the figure.

5

14P = 14 + 14 + 5 + 5 Add all side lengths.

or P = 2b + 2h

= 2(14) + 2(5)

Perimeter of rectangle.

= 38 units

= 28 + 10 = 38 units

Substitute 14 for b and 5 for h.

Pre-Algebra


6

11

Try This: Example 1A

A. Find the perimeter of the figure.

P = 11 + 11 + 6 + 6 Add all side lengths.

or P = 2b + 2h

= 2(11) + 2(6)

Perimeter of rectangle.

= 34 units

= 22 + 12 = 34 units


Pre-Algebra


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.

Helpful Hint

Pre-Algebra


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

20

16

= 72 units

P = 16 + 16 + 20 + 20

B. Find the perimeter of the figure.

Pre-Algebra


13

5

P = 5 + 5 + 13 + 13

= 36 units

Add all side lengths.

Try This: Example 1B

B. Find the perimeter of the figure.

Pre-Algebra


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.

Pre-Algebra


units2 units2

Pre-Algebra


A. (–1, –2), (2, –2), (2, 3), (–1, 3)

A = 15 units2

A = 3 • 5

A = bh

Additional Example 2A: Using a Graph to Find Area

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

Area of a rectangle.


Pre-Algebra


Try This: Example 2A

A. (–3, –2), (1, –2), (1, 3), (–3, 3)


A = 20 units2

A = 4 • 5

A = bhArea of a rectangle.

Substitute 4 for b and 5 for h.x

y

(–3, –2) (1, –2)

(1, 3)(–3, 3)

4

5

Pre-Algebra


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

Helpful Hint

Pre-Algebra


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

Additional Example 2B: Using a Graph to Find Area


A = 20 units2

A = 5 • 4

A = bhArea of a parallelogram.


Pre-Algebra


B. (–1, –1), (3, –1), (5, 3), (1, 3)

Try This: Example 2B


(5, 3)

x

y

(–1, –1) (3, –1)

(1, 3)

4

4

A = 16 units2

A = 4 • 4

A = bhArea of a parallelogram.


Pre-Algebra


Additional Example 3: Finding Area and Perimeter of a Composite Figure

Find the perimeter and area of the figure.

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

5 533

6

66

Pre-Algebra


5 533

6

Add the areas together.A = 6 • 5 + 6 • 2 + 6 • 5

= 30 + 12 + 30

= 72 units2

66

Additional Example 3 Continued

Pre-Algebra


Try This: Example 3

74

6

2

6

4

?

7 2

Find the perimeter of the figure.

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

= 42 units

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

2

Pre-Algebra


74

6

2

6

4

2

7 2

Find the area of the figure.

2

62

2

7

2 + 2

4

++

Add the areas together.

= 12 + 14 + 4 + 8

A = 2 • 6 + 7 • 2 + 2 • 2 + 4 • 2

= 38 units2

Try This: Example 3 Continued

22

Pre-Algebra


Lesson Quiz: Part 1

1. Find the perimeter of the figure.

12 ft

12 ft

4 ft5 ft

5 ft

5 ft

5 ft

44 ft

Pre-Algebra


Lesson Quiz: Part 2

2. Find the area of the figure.

108 ft2

12 ft

12 ft

4 ft5 ft

5 ft

5 ft

5 ft

Pre-Algebra


Lesson Quiz: Part 3

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

50 units2

3. (–4, 2), (6, 2), (6, –3), (–4, –3)

Pre-Algebra


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

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Pre-Algebra 6-1 Perimeter & Area of Rectangles & Parallelograms 6-1 Perimeter & Area of Rectangles & Parallelograms Pre-Algebra Warm Up Warm Up Problem