Transcript Course 3 Chapter 6 Lesson 1 - Guadalupe Elementary School

9-1 Perimeter & Area of Parallelograms
Warm Up
Graph the line segment for each set of
ordered pairs. Then find the length of
the line segment.
1. (–7, 0), (0, 0)
7 units
2. (0, 3), (0, 6)
3 units
3. (–4, –2), (1, –2) 5 units
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9-1 Perimeter & Area of Parallelograms
California
Standards
MG2.1 Use formulas routinely for finding
the perimeter and area of basic twodimensional figures and the surface area and
volume of basic three-dimensional figures,
including rectangles, parallelograms,
trapezoids, squares, triangles, circles, prisms,
and cylinders.
Also covered: MG2.2, MG2.4, and MG3.2
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9-1 Perimeter & Area of Parallelograms
Vocabulary
perimeter
area
base
height
composite figure
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9-1 Perimeter & Area of Parallelograms
Perimeter is the distance around a
polygon. To find the perimeter of any
polygon, you add the lengths of all its
sides.
Since opposite
sides of a
parallelogram are
equal in length,
you can find a
formula for the
perimeter of a
parallelogram.
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P=w+l+w+
l
=w+w+l +
l
= 2w + 2l
w
l
9-1 Perimeter & Area of Parallelograms
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9-1 Perimeter & Area of Parallelograms
A. Find the perimeter of the figure.
5
14
P = 2w + 2l
Perimeter of a parallelogram.
= 2(5) + 2(14) Substitute 5 for w and 14 for l.
= 10 + 28 = 38 units
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9-1 Perimeter & Area of Parallelograms
B. Find the perimeter of the figure.
16
P = 2w + 2l
20
Perimeter of a parallelogram.
= 2(16) + 2(20) Substitute 16 for w and 20 for l.
= 32 + 40 = 72 units
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9-1 Perimeter & Area of Parallelograms
The area of a plane figure is the number of unit
squares needed to cover the figure.(units squared)
The base of a parallelogram is the length of one
side.
The height is the perpendicular distance from the
base to the opposite side.
Height
Base
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Side
9-1 Perimeter & Area of Parallelograms
Holt CA Course 1
9-1 Perimeter & Area of Parallelograms
Graph and find the area of the figure with the
given vertices.
A. (–1, –2), (2, –2), (2, 3), (–1, 3)
Area of a rectangle.
A = bh
Substitute 3 for b and
5 for h.
A=3•5
A = 15 units2
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9-1 Perimeter & Area of Parallelograms
Caution!
The height of a parallelogram is not the length
of its slanted side. The height of a figure is
always perpendicular to the base.
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9-1 Perimeter & Area of Parallelograms
Graph and find the area of the figure with the
given vertices.
B. (0, 0), (5, 0), (6, 4), (1, 4)
Area of a parallelogram.
A = bh
Substitute 5 for b
and 4 for h.
A=5•4
A = 20 units2
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9-1 Perimeter & Area of Parallelograms
Graph and find the area of the figure with the
given vertices.
A. (–3, –2), (1, –2), (1, 3), (–3, 3)
y
(–3, 3)
(1, 3)
5
4
(–3, –2)
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Area of a rectangle.
A = bh
(1, –2)
x
Substitute 4 for b and
5 for h.
A=4•5
A = 20 units2
9-1 Perimeter & Area of Parallelograms
Graph the figure with the given vertices. Then
find the area of the figure.
B. (–1, –1), (3, –1), (5, 3), (1, 3)
y
(1, 3)
(5, 3)
4
(–1, –1)
Area of a parallelogram.
A = bh
4 (3, –1)
x
Substitute 4 for b
and 4 for h.
A=4•4
A = 16 units2
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9-1 Perimeter & Area of Parallelograms
A composite figure is made up of basic
geometric shapes such as rectangles,
triangles, trapezoids, and circles.
To find the area of a composite figure, find
the areas of the geometric shapes and
then add the areas.
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9-1 Perimeter & Area of Parallelograms
Find the perimeter.
6
5
6
3
6
3
5
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
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9-1 Perimeter & Area of Parallelograms
Find the Area:
6
5
6
3
6
3
5
A = 6 • 5 + 6 • 2 + 6 • 5 Add the areas together.
= 30 + 12 + 30
= 72 units2
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9-1 Perimeter & Area of Parallelograms
Find the perimeter.
The length of the side that is
not labeled is 2.
2
6
4
7
7
P=6+2+4+7+6+4+2+2+2+7 ?
= 42 units
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2
2
4
6
9-1 Perimeter & Area of Parallelograms
Find the area.
2
6
Add the areas together.
4
A=2•6+7•2+2•2+4•2
7
7
= 12 + 14 + 4 + 8
2 2
2
= 38 units2
2
4
6
7
+
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4
2
2
+
2 +
2
6
9-1 Perimeter & Area of Parallelograms
Lesson Quiz: Part I
1. Find the perimeter of the figure. 44 ft
2. Find the area of the figure.
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108 ft2
9-1 Perimeter & Area of Parallelograms
Lesson Quiz: Part II
Graph and find the area of each figure with
the given vertices.
3. (–4, 2), (6, 2), (6, –3), (–4, –3)
50 units2
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9-1 Perimeter & Area of Parallelograms
Lesson Quiz: Part III
Graph and find the area of each figure with
the given vertices.
4. (4, –2), (–2, –2), (–3, 5), (3, 5)
42 units2
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