8-4 area of parallelograms course 2 warm up problem of the day lesson presentation

8-4 Area of Parallelograms

Course 2

Warm Up

Problem of the Day

Lesson Presentation

Warm UpFind each product.

1. 8 12

2. 3

3. 9.4 6.3

4. 3.5 7

96

59.22

Course 2


12

5 13

18 23

24.5

Problem of the Day

How many 3 ft by 2 ft rectangles can you cut from one 8 ft by 4 ft rectangle? How much will be left over?

5 pieces; 2 ft2 left over

Course 2


Learn to find the area of rectangles and other parallelograms.

Course 2


Vocabulary

area

Insert Lesson Title Here

Course 2


Course 2


The area of a figure is the number of unit squares needed to cover the figure. Area is measured in square units.

AREA OF A RECTANGLE

The area A of a rectangle is the product of its length l and its width w.

A = lw w

l

Find the area of the rectangle.

Additional Example 1: Finding the Area of a Rectangle

Course 2


4.5 in.

7.4 in.

A = lw

A = 7.4 · 4.5

A = 33.3

The area of the rectangle is 33.3 in2.

Use the formula.

Substitute for l and w.

Multiply.

Find the area of the rectangle.

Course 2


6.3 in.

8.2 in.

A = lw

A = 8.2 · 6.3

A = 51.66

The area of the rectangle is 51.66 in2.

Use the formula.

Substitute for l and w.

Multiply.

Try This: Example 1

Course 2


For any parallelogram that is not a rectangle, you can cut a right triangle-shaped piece from one side and move it to the other side to form a rectangle.

The base of a parallelogram is the length of one side. The height of a parallelogram is the perpendicular distance from the base to the opposite side.

Base

Height Height

Base

Course 2


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

Helpful Hint

The area A of a parallelogramis the product of its base b and its height h.

AREA OF A PARALLELOGRAM

A = bh h

b

Find the area of the parallelogram.

Additional Example 2: Finding the Area of a Parallelogram

Course 2


8 m

16 m

A = bh

A = 16· 8

A = 128

The area of the parallelogram is128 m2.

Find the area of the parallelogram.

Course 2


6 cm

12 cm

A = bh

A = 12· 6

A = 72

The area of the parallelogram is72 cm2.

Try This: Example 2

A carpenter is using 2-ft by 2-ft square tiles to cover a rectangular floor. If the area of the floor is 150 ft2, what is the least number of tiles the carpenter will need?

Additional Example 3: Measurement Application

Course 2


First find the area of each tile.

A = lw Use the formula for the area of a square.

A = 2 · 2 Substitute 2 for l and 2 for w.

A = 4 Multiply.

The area of each square tile is 4 ft2.

Additional Example 3 Continued

Course 2


To find the number of tiles needed, divide the area of the floor by the area of one tile.

150 ft2

4 ft2= 37.5

Since covering the floor requires more than 37 tiles, the carpenter would need at least 38 tiles.

Try This: Example 3


Course 2

8-4 Area of parallelograms

Amanda decided to use 1.5-ft by 1.5-ft square tiles to cover a rectangular floor. If the area of the floor is 200 ft2, what is the least number of tiles Amanda will need?

First find the area of each tile.

A = lw Use the formula for the area of a square.

A = 1.5 · 1.5 Substitute 1.5 for l and 1.5 for w.

A = 2.25 Multiply.

The area of each square tile is 2.25 ft2.

Try This: Example 3 Continued


Course 2


To find the number of tiles needed, divide the area of the floor by the area of one tile.

200 ft2

2.25 ft2≈ 88.9

Since covering the floor requires more than 88 tiles, Amanda would need at least 89 tiles.

Lesson Quiz: Part 1

Find the area of each figure.

1. 2.

3.

24.5 ft2


84 ft2

Course 2


3.5 ft

7 ft

212

5 14

7 ft

12 ft41

2

612

ft

ft

ft

4.

1318

in2105 8 or

28 12

ft2

572

or

Lesson Quiz: Part 2

5. Suzanne is planning to use 1 ft by 0.5 ft tiles to finish her bathroom floor. If her floor is 7 ft by 10 ft, how many tiles will she need?

140 tiles


Course 2

8-4 Area of Parallelogram

8-4 area of parallelograms course 2 warm up problem of the day lesson presentation

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