Holt CA Course 1

9-1 Perimeter & Area of 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)

7 units

3 units

5 units

Holt CA Course 1

9-1 Perimeter & Area of Parallelograms

MG2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.Also covered: MG2.2, MG2.4, and MG3.2

California Standards

Holt CA Course 1

9-1 Perimeter & Area of Parallelograms

perimeter

area

base

height

composite figure

Vocabulary

Holt CA Course 1

9-1 Perimeter & Area of Parallelograms

Perimeter is the distance around a polygon. To find the perimeter of any polygon, you add the lengths of all its sides.

Since opposite sides of a parallelogram are equal in length, you can find a formula for the perimeter of a parallelogram.

P = w + l + w + l

= w + w + l + l

= 2w + 2l

w

l

Holt CA Course 1

9-1 Perimeter & Area of Parallelograms

Holt CA Course 1

9-1 Perimeter & Area of Parallelograms

A. Find the perimeter of the figure.

5

14

P = 2w + 2l

= 2(5) + 2(14)

Perimeter of a parallelogram.

= 10 + 28 = 38 units

Substitute 5 for w and 14 for l.

Holt CA Course 1

9-1 Perimeter & Area of Parallelograms

20

16

B. Find the perimeter of the figure.

P = 2w + 2l

= 2(16) + 2(20)

Perimeter of a parallelogram.

= 32 + 40 = 72 units

Substitute 16 for w and 20 for l.

Holt CA Course 1

9-1 Perimeter & Area of Parallelograms

The area of a plane figure is the number of unit squares needed to cover the figure.(units squared)

The base of a parallelogram is the length of one side.

The height is the perpendicular distance from the base to the opposite side.

HeightSide

Base

Holt CA Course 1

9-1 Perimeter & Area of Parallelograms

Holt CA Course 1

9-1 Perimeter & Area of Parallelograms

A. (–1, –2), (2, –2), (2, 3), (–1, 3)

A = 15 units2

A = 3 • 5

A = bh

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

Area of a rectangle.

Substitute 3 for b and 5 for h.

Holt CA Course 1

9-1 Perimeter & Area of Parallelograms

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!

Holt CA Course 1

9-1 Perimeter & Area of Parallelograms

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

A = 20 units2

A = 5 • 4

A = bh

Area of a parallelogram.

Substitute 5 for b and 4 for h.

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

Holt CA Course 1

9-1 Perimeter & Area of Parallelograms

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

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

Holt CA Course 1

9-1 Perimeter & Area of Parallelograms

B. (–1, –1), (3, –1), (5, 3), (1, 3)

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.

Holt CA Course 1

9-1 Perimeter & Area of Parallelograms

A composite figure is made up of basic geometric shapes such as rectangles, triangles, trapezoids, and circles.

To find the area of a composite figure, find the areas of the geometric shapes and then add the areas.

Holt CA Course 1

9-1 Perimeter & Area of Parallelograms

Find the perimeter.

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

Holt CA Course 1

9-1 Perimeter & Area of Parallelograms

5 533

6

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

= 30 + 12 + 30

= 72 units2

66

Find the Area:

Holt CA Course 1

9-1 Perimeter & Area of Parallelograms

74

6

2

6

4

?

7 2

Find the perimeter.

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

Holt CA Course 1

9-1 Perimeter & Area of Parallelograms

74

6

2

6

4

2

7 2

Find the area.

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

22

Holt CA Course 1

9-1 Perimeter & Area of Parallelograms

Lesson Quiz: Part I

1. Find the perimeter of the figure. 44 ft

2. Find the area of the figure. 108 ft2

Holt CA Course 1

9-1 Perimeter & Area of Parallelograms

Lesson Quiz: Part II

Graph and find the area of each figure with the given vertices.

50 units2

3. (–4, 2), (6, 2), (6, –3), (–4, –3)

Holt CA Course 1

9-1 Perimeter & Area of Parallelograms

Lesson Quiz: Part III

4. (4, –2), (–2, –2), (–3, 5), (3, 5)

42 units2

Graph and find the area of each figure with the given vertices.