Transcript Notes 42 - Mater Academy Lakes High School

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Changing Dimensions: Perimeter and Area
Additional Example 1: Comparing Perimeters and
Areas
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.
The smaller figure is a
2  1 in. rectangle.
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.
= 2(3) = 6
The perimeter is 6 in.
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.
Check It Out: Example 1
Find how the perimeter and area of the figure
change when its dimensions change.
8 in.
4 in.
2 in.
4 in.
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.
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?
Additional Example 3: Application
Mei works at a local diner whose speciality is
making pancakes. She makes silver dollar
pancakes with a diameter of 2 inches as well as
regular pancakes with a diameter double that of
the silver dollar pancakes. Does a regular
pancake have twice the area of a silver dollar
pancake? Explain. Use 3.14 for .
Find the area of each pancake and compare.
Silver: A = r2 Use the formula. Regular:
A  (1)2
Substitute for r.
A1
Evaluate the power.
A  3.14
Multiply.
A = r2
A  (2)2
A4
A  12.56
Additional Example 3 Continued
Mei works at a local diner whose speciality is
making pancakes. She makes silver dollar
pancakes with a diameter of 2 inches as well as
regular pancakes with a diameter double that of
the silver dollar pancakes. Does a regular
pancake have twice the area of a silver dollar
pancake? Explain. Use 3.14 for .
The area of the silver dollar pancake is 3.14 in2, and
the area of the regular pancake is 12.56 in2. When
the diameter is doubled, the area is 22, or 4, times
as great.
Check It Out: Example 3
Rae is designing a can for a new line of soup
products. The original can had a base diameter
of 7 cm and her new design will be double that
of the original base diameter. Will the new soup
can take up double the shelf space of the
original can? Explain. Use 3.14 for .