6-1
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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms6-1 Perimeter & Area of Rectangles
& Parallelograms
Pre-Algebra
Warm Up
Problem of the Day
Lesson Presentation
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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
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
Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
Problem of the DaySix pennies are placed around a seventh so that there are no gaps. What figure is formed by connecting the centers of the six outer pennies?
regular hexagon
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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
Learning Goal Assignment
Learn to find the perimeter and area of rectangles and parallelograms.
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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
perimeter
area
Vocabulary
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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
Perimeter is the distance around the outside of a figure. To find the perimeter of a figure, add the lengths of all its sides.
Height HeightSide
Base Base
Any side of a rectangle or parallelogram can be chosen as the base. The height is measured along a line perpendicular to the base.
Rectangle Parallelogram
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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
Additional Example 1A: Finding the Perimeter of Rectangles and Parallelograms
A. Find the perimeter of the figure.
5
14P = 14 + 14 + 5 + 5 Add all side lengths.
or P = 2b + 2h
= 2(14) + 2(5)
Perimeter of rectangle.
= 38 units
= 28 + 10 = 38 units
Substitute 14 for b and 5 for h.
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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
6
11
Try This: Example 1A
A. Find the perimeter of the figure.
P = 11 + 11 + 6 + 6 Add all side lengths.
or P = 2b + 2h
= 2(11) + 2(6)
Perimeter of rectangle.
= 34 units
= 22 + 12 = 34 units
Substitute 11 for b and 6 for h.
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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
The formula for the perimeter of a rectangle can be written as P = 2b + 2h, where b is the length of the base and h is the height.
Helpful Hint
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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
Additional Example 1B: Finding the Perimeter of Rectangles and Parallelograms
20
16
= 72 units
P = 16 + 16 + 20 + 20
B. Find the perimeter of the figure.
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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
13
5
P = 5 + 5 + 13 + 13
= 36 units
Add all side lengths.
Try This: Example 1B
B. Find the perimeter of the figure.
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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
Area is the number of square units in a figure. A parallelogram can be cut and the cut piece shifted to form a rectangle with the same base length and height as the original parallelogram. So a parallelogram has the same area as a rectangle with the same base length and height.
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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
units2 units2
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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
A. (–1, –2), (2, –2), (2, 3), (–1, 3)
A = 15 units2
A = 3 • 5
A = bh
Additional Example 2A: Using a Graph to Find Area
Graph the figure with the given vertices. Then find the area of the figure.
Area of a rectangle.
Substitute 3 for b and 5 for h.
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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
Try This: Example 2A
A. (–3, –2), (1, –2), (1, 3), (–3, 3)
Graph the figure with the given vertices. Then find the area of the figure.
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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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
The height of a parallelogram is not the length of its slanted side. The height of a figure is always perpendicular to the base.
Helpful Hint
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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
B. (0, 0), (5, 0), (6, 4), (1, 4)
Additional Example 2B: Using a Graph to Find Area
Graph the figure with the given vertices. Then find the area of the figure.
A = 20 units2
A = 5 • 4
A = bhArea of a parallelogram.
Substitute 5 for b and 4 for h.
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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
B. (–1, –1), (3, –1), (5, 3), (1, 3)
Try This: Example 2B
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 = bhArea of a parallelogram.
Substitute 4 for b and 4 for h.
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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
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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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
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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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
Try This: Example 3
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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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
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
Try This: Example 3 Continued
22
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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
Lesson Quiz: Part 1
1. Find the perimeter of the figure.
12 ft
12 ft
4 ft5 ft
5 ft
5 ft
5 ft
44 ft
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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
Lesson Quiz: Part 2
2. Find the area of the figure.
108 ft2
12 ft
12 ft
4 ft5 ft
5 ft
5 ft
5 ft
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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
Lesson Quiz: Part 3
Graph the figure with the given vertices and find its area.
50 units2
3. (–4, 2), (6, 2), (6, –3), (–4, –3)
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Pre-Algebra
6-1 Perimeter & Area of Rectangles & Parallelograms
Lesson Quiz: Part 4
Graph the figure with the given vertices and find its area.
4. (4, –2), (–2, –2), (–3, 5), (3, 5)
42 units2