9-1 Area of Rectangles and Parallelograms

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Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

9-1 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

9-1 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

9-1 Area of Rectangles and Parallelograms

MA.6.A.3.4 Solve problems given a formula.

Also MA.6.A.4.2

Sunshine State Standards

9-1 Area of Rectangles and Parallelograms

Vocabulary

area

9-1 Area of Rectangles and Parallelograms

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

9-1 Area of Rectangles and Parallelograms

Additional Example 1: Estimating the Area of an Irregular Figure

Estimate the area of the figure.

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

9-1 Area of Rectangles and Parallelograms

Check It Out: Example 1

Estimate the area of the figure.

about 18 mi2.

= 1mi2

9-1 Area of Rectangles and Parallelograms

9-1 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 and 9 for w.Multiply.

A = lw

A = 15 • 9

A = 135

The area is about 135 in2.

15 in.

9 in.

9-1 Area of Rectangles and Parallelograms

Check It Out: Example 2A

Find the area of each rectangle..

70 ft.

11 ft.

A = lw = 70 × 11 = 770The area is 770 ft .2

9-1 Area of Rectangles and Parallelograms

Check It Out: Example 2B

Find the area of each rectangle..

9 mi.

12 mi.

A = lw = 12 × 9 = 108The area is 108 mi.2

9-1 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.

9-1 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

9-1 Area of Rectangles and Parallelograms

Check It Out: Example 3A

Find the area of each parallelogram.

8 ft

7 ft

A = bh = 8 × 7 = 56The area is 56 ft .2

9-1 Area of Rectangles and Parallelograms

Check It Out: Example 3B

Find the area of each parallelogram.

12 m

5.6 m

A = bh = 5.6 × 12 = 67.2The area is 67.2 m .2

9-1 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

9-1 Area of Rectangles and Parallelograms

Check It Out: 4

What is the area that will be painted?

18 × 8 = 144;3 × 2.5 = 7.5;144 - (3 × 7.5) = 144 - 22.5 The area that will be painted is 121.5 ft .2

18 ft

3 ft

2.5 ft

8 ft

= 121.5

The figure shows a wall of an office with three identical windows. An employee is going to paint this wall of the office