10-4 Comparing Perimeter and Area
Warm Up
Problem of the Day
Lesson Presentation
Course 1
10-4 Comparing Perimeter and Area
Warm Up
1. What is the area of a figure made up of a
rectangle with length 12 cm and height 4
cm and a parallelogram with length 12 cm
120 cm2
and height 6 cm?
2. What is the area of a figure consisting of
a triangle sitting on top of a rectangle?
The triangle has a base of 12 in. and
height of 9 in., and the rectangle has a
base of 12 in. and height of 5 in. 114 in2
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10-4 Comparing Perimeter and Area
Problem of the Day
If sixteen people sit, evenly spaced, in a
circle for story time, who sits directly
across from person 5?
person 13
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10-4 Comparing Perimeter and Area
Learn to make a model to explore how
area and perimeter are affected by
changes in the dimensions of a figure.
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10-4 Comparing Perimeter and Area
Additional Example 1: Changing Dimensions
Find how the perimeter and the area of the
figure change when its dimensions change.
= 1 inch
Draw a model of the two figures on graph paper.
Label the dimensions.
The original figure is
a 4  2 in. rectangle.
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The smaller figure is a
2  1 in. rectangle.
10-4 Comparing Perimeter and Area
Additional Example 1 Continued
Find how the perimeter and the area of the
figure change when its dimensions change.
Use the formula for perimeter of a rectangle.
P = 2(l + w)
P = 2(l + w).
Substitute for l and w.
= 2(4 + 2)
= 2(2 + 1)
Simplify.
= 2(6) = 12
The perimeter is 12 in.
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= 2(3) = 6
The perimeter is 6 in.
10-4 Comparing Perimeter and Area
Additional Example 1 Continued
Find how the perimeter and the area of the
figure change when its dimensions change.
Use the formula for area of a rectangle.
A = lw
A = lw
Substitute for l and w.
=4x2
=8
Simplify.
The area is 8 in2.
=2x1
=2
The area is 2 in2.
The perimeter is divided by 2, and the area is
divided by 4.
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10-4 Comparing Perimeter and Area
Check It Out: Example 1
Find how the perimeter and the area of the
figure change when its dimensions change.
= 1 inch
Draw a model of the two figures on graph paper.
Label the dimensions.
The original figure is
2 x 2 in. rectangle.
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The larger figure is a
4 x 4 in. rectangle.
10-4 Comparing Perimeter and Area
Check It Out: Example 1 Continued
Find how the perimeter and the area of the
figure change when its dimensions change.
Use the formula for perimeter of a rectangle.
P = 2(l + w)
P = 2(l + w).
Substitute for l and w.
= 2(2 + 2)
= 2(4 + 4)
Simplify.
= 2(4) = 8
The perimeter is 8 in.
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= 2(8) = 16
The perimeter is 16 in.
10-4 Comparing Perimeter and Area
Check It Out: Example 1 Continued
Find how the perimeter and the area of the
figure change when its dimensions change.
Use the formula for area of a rectangle.
A = lw
A = lw
Substitute for l and w.
=2x2
=4
Simplify.
The area is 4 in2.
=4x4
= 16
The area is 16 in2.
The perimeter is multiplied by 2, and the area is
multiplied by 4.
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10-4 Comparing Perimeter and Area
Additional Example 2: Application
Draw a rectangle whose dimensions are 4 times
as large as the given rectangle. How do the
perimeter and area change?
12 cm
2 cm
3 cm
8 cm
Multiply each dimension by 4.
P = 10 cm
P = 40 cm
A = 6 cm2
A = 96 cm2
When the dimensions of the rectangle are multiplied
by 4, the perimeter is multiplied by 4, and the area
is multiplied by 16, or 42.
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10-4 Comparing Perimeter and Area
Check It Out: Example 2
Draw a rectangle whose dimensions are 2 times
as large as the given rectangle. How do the
perimeter and area change?
10 cm
5 cm
6 cm
3 cm
Multiply each dimension by 2.
P = 16 cm
P = 32 cm
A = 15 cm2
A = 60 cm2
When the dimensions of the rectangle are multiplied
by 2, the perimeter is multiplied by 2, and the area
is multiplied by 4, or 22.
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10-4 Comparing
Insert Lesson
Perimeter
Title Here
and Area
Lesson Quiz
Find how the perimeter and area of the
triangle change when its dimensions change.
The perimeter is multiplied by 2, and the area is
multiplied by 4; perimeter = 24, area = 24;
perimeter = 48, area = 96.
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