Lesson 4.5
Core Focus on Decimals
& Fractions
Perimeter with Fractions
Warm-Up
1. Simplify 1 164 inches .
1 14 inches
2. 3 12  2 34
6 14
3
3. 4 18  3 16
7 165
15
4. 8 14  6 16
15 163
Lesson 4.5
Perimeter with Fractions
Add lengths, including fractions and
mixed numbers, of the sides of polygons
to find perimeters.
Vocabulary
Perimeter
The distance around a closed figure.
Polygon
A closed figure formed by three or more line segments.
Finding Perimeter
1. Measure all sides (if necessary).
2. Add the lengths of all sides together.
Example 1
Find the perimeter of the rectangle in inches.
Use a ruler to measure each side of the shape to the nearest
sixteenth of an inch.
3
Length = in
4
Add all sides.
Simplify.
The perimeter is 2 inches.
12 3

16 4
1
Width = in
4
3 1 3 1 8
    2
4 4 4 4 4
Opposite sides of
rectangles are the
same length.
4 1

16 4
Example 2
Use the given measurements to find the perimeter
of the polygon.
Add the lengths of all sides together.
1 18 
5 5
5 5
  1 18  
16 16
16 16
Change the mixed numbers to
improper fractions.
1 18 
9
8
Use the LCD to rename the fractions.
The LCD is 16.
9 18

8 16
Add the sides of the polygon.
18 5 5 18 5 5 56
     
16 16 16 16 16 16 16
Simplify.
56 7
  3 12
16 2
The perimeter of the polygon is 3 12 inches.
Example 3
Brayden went for a walk. He walked in a rectangular pattern around a city
block. First he walked 66 23 yards. He turned right and walked 76 16 yards. He
turned right two more times and ended up where he started. What was the
perimeter of the city block?
Brayden walked in a rectangular pattern.
Add the four sides.
66 23  76 16  66 32  76 16  ? yards
66 23  66 64
Use the LCD to rename the fractions.
The LCD is 6.
Add the sides of the city block.
66 64  76 16  66 64  76 16  284 106
Simplify.
10
 1 64  284  1 64  285 64  285 23
6
The perimeter of the city block Brayden walked was
285 23 yards.
Example 4
Use the given measurement to find the perimeter
of the square.
Add all four sides of the
square together.
1 12  1 12  1 12  1 12  4 42
All sides of a square
are the same length.
Simplify.
4 42  4  2  6
The perimeter of the square is 6 inches.
Communication Prompt
Why should you know how to find the perimeter
of an object?
Exit Problems
1. What is the perimeter of a rectangle that is 2 85 inches long
and 1 12 inches wide?
8 14 inches
2. What is the perimeter of a triangle with sides that measure:
3 14 inches, 4 12 inches and 5 12 inches?
13 14 inches
3. What is the perimeter of a square with a side that measures
7
inch?
8
3 12 inches