Transcript Columbus State Community College

Columbus State Community College
Chapter 3 Section 1
Problem Solving: Perimeter
Ch 3 Sec 1: Slide #1
Problem Solving: Perimeter
1. Use the formula for perimeter of a square to find the
perimeter or the length of one side.
2. Use the formula for perimeter of a rectangle to find the
perimeter, the length, or the width.
3. Find the perimeter of parallelograms, triangles, and irregular
shapes.
Ch 3 Sec 1: Slide #2
Perimeter
Perimeter
The distance around the outside edges of any flat shape is called the
perimeter of the shape.
Ch 3 Sec 1: Slide #3
Review of a Square


A square has four sides that are all the same length.
The sides of a square meet to form right angles, which
measure 90°. This means that the sides form “square corners.”
in. is the short way
to write inches.
5 in.
5 in.
In
if square
one right
Thea square,
small red
angle
is shown,
indicates
a right the
angle
other
three angles are
(90° angle).
5 in.
also right angles.
5 in.
Ch 3 Sec 1: Slide #4
Finding the Perimeter of a Square
To find the perimeter of a square, we can “unfold” the shape so the
four sides lie end-to-end, as shown below.
7 cm cm is the short way to
NOTE:
7 cm write centimeters.
7 cm
7 cm 7 cm
7 cm 7 cm
Now we can see the total length of the four sides. The total length is
the perimeter of the square. We can find the perimeter by adding.
Perimeter = 7 cm + 7 cm + 7 cm + 7 cm = 28 cm
or
Perimeter = 4 ( 7 cm ) = 28 cm
Ch 3 Sec 1: Slide #5
Perimeter of a Square
Finding the Perimeter of a Square
Perimeter of a square = side + side + side + side
or
P = 4 • side
P = 4s
Ch 3 Sec 1: Slide #6
Finding the Perimeter of a Square
EXAMPLE 1
Finding the Perimeter of a Square
Find the perimeter of a square that measures 15 yards on each side.
Use the formula for perimeter, P = 4s.
P = 4s
Formula for perimeter of a square.
P = 4 • 15 yd
Replace s with 15 yd. Multiply 4 times 15 yd.
P = 60 yd
Write 60 yd; yd is the unit of measure.
The perimeter of the square is 60 yards.
Ch 3 Sec 1: Slide #7
Finding the Length of One Side of a Square
EXAMPLE 2
Finding the Length of One Side of a Square
If the perimeter of a square is 36 m, find the length of one side.
P = 4s
Formula for perimeter of a square.
36 m = 4 s
Replace P with 36 cm
36 m = 4 s
4
4
Divide both sides by 4.
9m =
s
The length of one side of the square is 9 m.
Ch 3 Sec 1: Slide #8
Review of a Rectangle


A rectangle has four sides that meet to form right angles (90°).
Each set of opposite sides is parallel and congruent (has the
same length).
90° angles
90° angles
Ch 3 Sec 1: Slide #9
Review of a Rectangle
width
7 in.
21 in.
length
width
In a rectangle, if one right angle is shown,
the other three angles are also right angles.
7 in.
length
21 in.
Perimeter = 21 in. + 7 in. + 21 in. + 7 in. = 56 in.
Ch 3 Sec 1: Slide #10
Finding the Perimeter of a Rectangle
Finding the Perimeter of a Rectangle
Perimeter of a rectangle = length + length + width + width
or
P = ( 2 • length ) + ( 2 • width )
P =
2l
+
2w
Ch 3 Sec 1: Slide #11
Finding the Perimeter of a Rectangle
EXAMPLE 3
Finding the Perimeter of a Rectangle
Find the perimeter of this rectangle.
12 m
P = 2l
3m
3m
12 m
+ 2w
P = 2 ( 12 m ) + 2 ( 3 m )
P = 24 m
P =
+ 6m
30 m
Ch 3 Sec 1: Slide #12
Finding the Length or Width of a Rectangle
EXAMPLE 4
Finding the Length or Width of a Rectangle
If the perimeter of a rectangle is 86 inches and the width is 9 inches,
find the length.
P = 2l + 2w
86 in. = 2 l + 2 ( 9 in. )
?
86 in. = 2 l + 18 in.
9 in.
9 in.
– 18 in.
– 18 in.
?
68 in. = 2 l
2
2
34 in. =
l
The length of the rectangle is 34 inches.
Ch 3 Sec 1: Slide #13
Finding the Length or Width of a Rectangle
EXAMPLE 4
Finding the Length or Width of a Rectangle
If the perimeter of a rectangle is 86 inches and the width is 9 inches,
find the length.
Check Put the length measurements on your sketch.
34 in.
P = 34 in. + 34 in. + 9 in. + 9 in.
9 in.
9 in.
P = 86 in.
34 in.
A perimeter of 86 inches matches the information in the original
problem, so 34 inches is the correct length of the rectangle.
Ch 3 Sec 1: Slide #14
Parallelograms
A parallelogram is a four-sided figure in which opposite sides are
both parallel and equal in length.
A
B
AD
AB is parallel to DC
BC
D
C
Ch 3 Sec 1: Slide #15
Finding the Perimeter of a Parallelogram
EXAMPLE 5
Finding the Perimeter of a Parallelogram
Find the perimeter of the parallelogram below.
5 yd
P = 5 yd + 5 yd + 21 yd + 21 yd
21 yd
21 yd
P = 52 yd
5 yd
Ch 3 Sec 1: Slide #16
Finding the Length of a Side of an Irregular Shape
EXAMPLE 6
Finding the Length – Irregular Shapes
Find the length of the unlabeled side if the perimeter is 52 feet.
16 ft
4 ft
10 ft
?
9 ft
6 ft
52 ft = 16 ft + 4 ft + x ft + 6 ft + 9 ft + 10 ft
52 ft = x + 45 ft
– 45 ft
– 45 ft
7 ft = x
The length of the unlabeled side is 7 feet.
Ch 3 Sec 1: Slide #17
Problem Solving: Perimeter
Chapter 3 Section 1 – Completed
Written by John T. Wallace
Ch 3 Sec 1: Slide #18