8-1 Perimeter & Area of Rectangles & Parallelograms Course 3 Warm Up Warm Up Problem of the...

8-1 Perimeter & Area of Rectangles & Parallelograms

Course 3

Warm Up

Problem of the Day

Lesson Presentation

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

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms

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

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms

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

Course 3

Perimeter and Area of Rectangles and Parallelograms

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms

perimeter

area

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms

Vocabulary

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.

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms

Rectangle Parallelogram

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

Find the perimeter of the figure.

5

14

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms

P = 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.

When referring to the measurements of a rectangle, the terms length (l) and width (w) are sometimes used in place of base (b) and height (h). So the formula for the perimeter of a rectangle can be written as

P = 2b + 2h = 2l + 2w = 2(l + w).

Caution!

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms

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

20

16

= 72 units

P = 16 + 16 + 20 + 20

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms

Find the perimeter of the figure.

Add all side lengths.

6

11

Check It Out: Example 1A

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms

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

Substitute 11 for b and 6 for h.

13

5

P = 5 + 5 + 13 + 13

= 36 units

Add all side lengths.

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms

Check It Out: Example 1B

Find the perimeter of the figure.

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms

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.

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms

The formula for the area of a rectangle can also be written as A = lw.

Helpful Hint

(–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

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms

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

Area of a rectangle.

Substitute 3 for b and 5 for h.

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

Caution!

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms

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

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms

Additional Example 2B: Using a Graph to Find Area

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

A = 20 units2

A = 5 • 4

A = bh

Area of a parallelogram.

Substitute 5 for b and 4 for h.

Check It Out: Example 2A

(–3, –2), (1, –2), (1, 3), (–3, 3)

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms

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

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

(–1, –1), (3, –1), (5, 3), (1, 3)

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms

Check It Out: Example 2B

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

(5, 3)

x

y

(–1, –1) (3, –1)

(1, 3)

4

4

A = 16 units2

A = 4 • 4

A = bh

Area of a parallelogram.

Substitute 4 for b and 4 for h.

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

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms

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

5 533

6

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

= 30 + 12 + 30

= 72 units2

66

Additional Example 3 Continued

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms

Check It Out: 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

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms

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

2

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

Check It Out: Example 3 Continued

2

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms

2

Lesson Quiz: Part I

1. Find the perimeter of the figure.

12 ft

12 ft

4 ft5 ft

5 ft

5 ft

5 ft

44 ft

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms

Lesson Quiz: Part II

2. Find the area of the figure. 108 ft2

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms

12 ft

12 ft

4 ft5 ft

5 ft

5 ft

5 ft

Lesson Quiz: Part III

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

50 units2

3. (–4, 2), (6, 2), (6, –3), (–4, –3)

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms

Lesson Quiz: Part IV

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

4. (4, –2), (–2, –2), (–3, 5), (3, 5)

42 units2

Course 3

8-1 Perimeter & Area of Rectangles & Parallelograms