8-4 area of parallelograms course 2 warm up problem of the day lesson presentation
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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
8-4 Area of Parallelograms
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
8-4 Area of Parallelograms
Learn to find the area of rectangles and other parallelograms.
Course 2
8-4 Area of Parallelograms
Vocabulary
area
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Course 2
8-4 Area of Parallelograms
Course 2
8-4 Area of Parallelograms
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
8-4 Area of Parallelograms
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
8-4 Area of Parallelograms
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
8-4 Area of Parallelograms
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
8-4 Area of Parallelograms
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
8-4 Area of Parallelograms
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
8-4 Area of Parallelograms
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
8-4 Area of Parallelograms
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
8-4 Area of Parallelograms
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
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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
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Course 2
8-4 Area of Parallelograms
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
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84 ft2
Course 2
8-4 Area of Parallelograms
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
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Course 2
8-4 Area of Parallelogram