10-1 Area of Rectangles and Parallelograms

Warm UpWarm Up

Lesson Presentation

Problem of the Day

Lesson Quizzes

10-1 Area of Rectangles and Parallelograms

Warm Up

1. What is the perimeter of a square with side lengths of 15 in.?

2. What is the perimeter of a rectangle with length 16 cm and width 11 cm?

60 in.

54 cm

10-1 Area of Rectangles and Parallelograms

Problem of the Day

Two wibbles equal four wabbles, and eight wabbles equal two bibbles. If a square has a perimeter of 16 wibbles, what is its area in square bibbles?

4 square bibbles

10-1 Area of Rectangles and Parallelograms

Learn to estimate the area of irregular figures and to find the area of rectangles and parallelograms.

10-1 Area of Rectangles and Parallelograms

Vocabulary

area

10-1 Area of Rectangles and Parallelograms

The area of a figure is the amount of surface it covers. We measure area in square units.

10-1 Area of Rectangles and Parallelograms

Additional Example 1: Estimating the Area of an Irregular Figure

Find the area of the rectangle.

Count full squares: 19 red squares.

Count almost-full squares: 9 blue squares.Count squares that are about half-full: 4 green squares = 2 full squares.Do not count almost empty yellow squares.Add. 19 + 9 + 2 = 30

The area of the figure is about 30 mi .2

10-1 Area of Rectangles and Parallelograms

Check It Out: Example 1

Estimate the are of the figure.

Count full squares: 11 red squares.

Count almost-full squares: 5 green squares.Count squares that are about half-full: 4 blue squares = 2 full squares.Do not count almost empty yellow squares.Add. 11 + 5 + 2 = 18

The area of the figure is about 18 mi2.

= mi2

10-1 Area of Rectangles and Parallelograms

10-1 Area of Rectangles and Parallelograms

Additional Example 2: Finding the Area of a Rectangle

Find the area of the figure.

Write the formula.

Substitute 15 for l.Substitute 9 for w.

A = lw

A = 15 • 9

A = 135

The area is about 135 in2.

15 in.

9 in.

10-1 Area of Rectangles and Parallelograms

Check It Out: Example 2

Find the area of the figure.

Write the formula.

Substitute 13 for l.Substitute 7 for w.

A = lw

A = 13 • 7

A = 91

The area is about 91 in2.

13 in.

7 in.

10-1 Area of Rectangles and Parallelograms

You can use the formula for the area of a rectangle to write a formula for the area of a parallelogram. Imagine cutting off the triangle drawn in the parallelogram and sliding it to the right to form a rectangle.

The area of a parallelogram = bh. The area of a rectangle = lw.

The base of the parallelogram is the length of the rectangle. The height of the parallelogram is the width of the rectangle.

10-1 Area of Rectangles and Parallelograms

Additional Example 3: Finding the Area of a Parallelogram

Find the area of the parallelogram.

Write the formula.

Multiply.

A = bh

2 ft12

A = 2 • 112__ 1

4__ Substitute 2 for b

and 1 for h.

12__

14__

A = •52__ 5

4__

A = or 325 8

___ 18__

The area is 3 ft2. 18__

14

1 ft

10-1 Area of Rectangles and Parallelograms

Check It Out: Example 3

Find the area of the parallelogram.

Write the formula.

Multiply.

A = bh

A = 1 • 312__ 1

2__ Substitute 1 for b

and 3 for h.

12__

12__

A = •32__ 7

2__

A = or 521 4

___ 14__

The area is 5 ft2.14__

11 ft2

13 ft2

10-1 Area of Rectangles and Parallelograms

Additional Example 4: Recreation Application

Jessika is going to tile a kitchen that measures 13 ft by 17 ft. Some floor space is taken up by an island that measures 3 ft by 6 ft. How much area remains to be tiled in the kitchen?

Substitute for l and w in A = lw.

Use the order of operations.

The area of the kitchen to be tiled is 203 ft2.

floor area

To find the area to be tiled, subtract the area of the island from the area of the floor.

kitchen area to be tiledisland– =

(13 • 17) (3 • 6) n– =

221 – 18 = 203

10-1 Area of Rectangles and Parallelograms

Check It Out: Example 4

Miguel is going to landscape his backyard that measures 16 ft by 11 ft. Some of the backyard space is taken up by a built-in BBQ that measures 2 ft by 4 ft. How much area remains to be landscaped?

Substitute for l and w in A = lw. Use the order of operations.

The area of the backyard to be landscaped is 168 ft2.

backyard area

To find the landscaped area, subtract the area of the BBQ from the area of the backyard.

landscaped areaBBQ– =

(16 • 11) (2 • 4) n– =

176 – 8 = 168

10-1 Area of Rectangles and Parallelograms

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

10-1 Area of Rectangles and Parallelograms

Lesson Quiz

Find the area of each figure.

1. 2.

3. What is the area of a parallelogram with base 16

in. and height 10 in.?

4. A square fish pond that is 6 ft long is

surrounded by a square walk that is 18 ft long.

What is the area covered by the walk?

41.4 m2 48 ft2

160 in2

288 ft2

10-1 Area of Rectangles and Parallelograms

1. Find the area of the figure.

A. 53.9 m2 B. 53.9 m2

C. 54.6 m2 D. 54.9 m2

Lesson Quiz for Student Response Systems

10-1 Area of Rectangles and Parallelograms

2. Find the area of the figure.

A. 60 ft2 B. 70 ft2

C. 80 ft2 D. 90 ft2

Lesson Quiz for Student Response Systems

10-1 Area of Rectangles and Parallelograms

3. Find the area of a parallelogram with base 19 ft and height 11 ft.

A. 209 ft2 B. 214 ft2

C. 216 ft2 D. 220 ft2

Lesson Quiz for Student Response Systems