Holt CA Course 1 9-1 Perimeter & Area of Parallelograms Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

Holt CA Course 1

9-1 Perimeter & Area of Parallelograms

Warm Up

California StandardsCalifornia Standards

Lesson Presentation

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Holt CA Course 1


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

Holt CA Course 1


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

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perimeter

area

base

height

composite figure

Vocabulary

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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


Holt CA Course 1


Additional Example 1: Finding the Perimeter 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.

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Additional Example 1: Finding the Perimeter of Parallelograms

20

16

B. Find the perimeter of the figure.

P = 2w + 2l

= 2(16) + 2(20)


= 32 + 40 = 72 units


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6

11

Check It Out! Example 1

A. Find the perimeter of the figure.

P = 2w + 2l

= 2(6) + 2(11)


= 12 + 22 = 34 units


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13

5


B. Find the perimeter of the figure.

P = 2w + 2l

= 2(5) + 2(13)


= 10 + 26 = 36 units


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The area of a plane figure is the number of unit squares needed to cover the figure. 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

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While perimeter is expressed in linear units, such as inches (in.) or meters (m), area is expressed in square units, such as square feet (ft2).

You can cut a parallelogram and shift the cut piece to form a rectangle whose base and height are the same as those of the original parallelogram. The same number of unit squares are needed to cover the two figures. So a parallelogram and a rectangle that have the same base and height have the same area.

Holt CA Course 1


Holt CA Course 1


Since the base and height of a rectangle are the same as its length and width, the formula for the area of a rectangle can also be written as A = lw.

Helpful Hint

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A. (–1, –2), (2, –2), (2, 3), (–1, 3)

A = 15 units2

A = 3 • 5

A = bh

Additional Example 2: Using a Graph to Find Area

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

Area of a rectangle.

Substitute 3 for b and 5 for h.

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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!

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

Additional Example 2: Using a Graph to Find Area

A = 20 units2

A = 5 • 4

A = bh

Area of a parallelogram.



Holt CA Course 1

9-1 Perimeter & Area of ParallelogramsCheck It Out! Example 2

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


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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.


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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.

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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

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5 533

6

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

= 30 + 12 + 30

= 72 units2

66

Additional Example 3 Continued

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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

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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

22

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Lesson Quiz: Part I

1. Find the perimeter of the figure. 44 ft

2. Find the area of the figure. 108 ft2

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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)

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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.

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Holt CA Course 1 9-1 Perimeter & Area of Parallelograms Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview