Perimeter, Area, Volume

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Lesson 19

• Perimeter, Area, Volume

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Some GEPA questions apply percent to areas of
squares and circles. This shows the
interrelationship of percent, algebra, and
geometry, as illustrated in the following example.
Example 1 What is the best estimate of the
shaded portion on the diagram below? A. 10 B.
20 C. 40 D. 80
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This is equivalent to solving the following
problem The area of the circle is what
percent of the area of the square?
1. Find the area of the circle. Use A pi r2
4 ft.
A pi r2 A 3.14 2ft 2ft A 3.14
4ft2 A 12.56 ft2
radius
2ft .
you're not done yet!
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2. Find the area of the square. Use A s2
A s2 A 8ft 8ft A 64 ft2
8ft
8ft
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3. Write an equation
Area of circle is what percent of area of square?
12.56 ft2

x
64

12.56 ft2

64
x
(divide each side by 64)

x
0.19625
Round 0.19625 to 0.20. Write as percent
20
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The next application involves the distance around
a circle circumference of a circle.
The formula for the circumference of a circle C
2 pi r
Example 2 The diagram below represents a
racetrack in the shape of a rectangle with a
semicircle at each end. Find the total distance
around the track.
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The total distance around the track is 200 ft
200 ft distance around each semicircle.
Separate the two semicircles from the rectangle.
Put them together to get the whole Circle with
radius 25 ft.
Distance around track is
200 ft 200 ft circumference of circle 200 ft
200 ft 2 pi r 200 ft 200 ft 2 3.14
25 ft 200 ft 200 ft (50 3.14) ft 400 ft
157 ft 557 ft
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Sometimes the area of a more complex figure can
be found by breaking it up into several
rectangles or squares. Then the area of the
original figures will be the sum of the areas of
the smaller rectangles and squares.
First of all, note that the cost of carpeting a
room is computed for the number of square yards
of area, NOT the number of square feet.
Recall that 3 ft 1 yd.
or
So, from the drawing at the right, 1 yd2 9 ft2
1 square yard 9 square feet
1 yd 1 yd 3 ft 3 ft
1 yd2 9 ft2
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Example 3 The floor plan below shows the
measurements of a living room in feet. Find the
minimum number of square yards of carpeting
needed to carpet the entire floor wall to
wall. A. 27 yards2 B. 28 yards2 C. 248
yards2 D. 298 yards2
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1. Find the missing side lengths
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10
12
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Example 3 The floor plan below shows the
measurements of a living room in feet. Find the
minimum number of square yards of carpeting
needed to carpet the entire floor wall to
wall. A. 27 yards2 B. 28 yards2 C. 248
yards2 D. 298 yards2
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1. Find the missing side lengths
18
4
10
12
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Example 3 The floor plan below shows the
measurements of a living room in feet. Find the
minimum number of square yards of carpeting
needed to carpet the entire floor wall to
wall. A. 27 yards2 B. 28 yards2 C. 248
yards2 D. 298 yards2
16
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1. Find the missing side lengths
18
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2. Separate the figure into 2 rectangles.
10
12
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Separate the figure into 2 rectangles.
8 x 16 128
10 x 12 120
12 x 18 216
8 x 4 32
Total area 32 216 248
Total area 128 120 248
you're not done yet!
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Total area 128 120 248
This is the area in square feet.
Convert this to square yards, since that is what
is called for in the problem.
There are 9 square feet in one square yard.
Find how many 9s there are in 248.
Divide 248 9 27.55555556
The carpet store can not give you a decimal or
fraction part of a yard, You need the next higher
whole number of yards 28.
28 yd2
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VOLUME
The formula for volume V L W H
Example What is the volume of a
rectangle solid measuring 12 cm wide by 7 cm
long by 4 cm high?
V L W H
V 12 7 4 cm cm cm
V 336 cm3
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Mr. Miller has 640 ft3 of water in his in ground
pool. The pool is 4 ft deep (high) and 20 ft
long. How wide is the pool?
A. 8 ft B. 24 ft C. 80 ft D. 160 ft
Since 640 ft3 indicates volume, use the volume
formula to write an equation.
V L W H
640


4
20

W
(divide each side by 80)
640 80W
8 W
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Surface Area
The total surface area of a rectangle solid is
the sum of the areas of the 6 faces, or double
the area of the 3 faces you can see.
Example Find the total surface area of
the rectangular solid. A. 27 cm2 B. 47 cm2
C. 60 cm2 D 94 cm2
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Surface Area
The total surface area of a rectangle solid is
the sum of the areas of the 6 faces, or double
the area of the 3 faces you can see.
Example Find the total surface area of
the rectangular solid. A. 27 cm2 B. 47 cm2
C. 60 cm2 D 94 cm2
A 2 (3 cm 4 cm) 2 (4 cm 5 cm) 2
( 5 cm 3 cm)
A 94 cm2
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