What is Perimeter?
Definition: Perimeter is defined as the path or boundary that surrounds a shape in geometry. It can also be described as the length of a geometric shape’s outline.
How to Find the Perimeter by Counting units
Count the units, that is, the sides of the unit squares, to find the perimeter.
Let us take an example to understand how we can find the perimeter by counting the unit squares.
What is the Perimeter of the given Shape?
Each grid is a unit square.
Count the units as you go around the figure.
There are 10 units around the figure.
As a result, the perimeter is 10 units.
How to Find the perimeter using an inch scale and a centimeter scale
First, let us understand how we can measure length using a ruler.
A ruler has two sides with two different units of measurement: centimeters and inches. The following are the steps to measure length with a ruler:
Step 1: Decide on the unit of the length measurement. If you want a value in centimeters, use the side of the ruler that has markings in centimeters. And if you are working with inches as the unit, use the inch side of the ruler.
Step 2: Starting at point 0, place the object beside the ruler.
Step 3: Determine the value of the endpoint. The length of the pencil, for example, ranges from 0 to “8” cm as in the diagram. When measured on the inch side, we can see that the length corresponds to around 3.2 inches.
Hence, the length of the pencil is 8 centimeters, or approximately 3.2 inches.
Similarly, the lengths of the sides of various shapes can be found and added to calculate the perimeter of that particular shape.
What is a Polygon?
In geometry, a polygon is a two-dimensional closed shape with straight sides that are flat or a plane. There are no curved sides to it. The edges of a polygon are also known as the sides. The vertices or corners of a polygon are the points where two sides meet.
Finding the Perimeter of a Polygon
Let us take an example to understand how we can find the perimeter of a polygon.
Example:
Determine the perimeter of the rhombus.
Solution:
All the sides of a rhombus are equal.
Method One:
The perimeter is calculated by adding the lengths of the shape’s sides.
P = 6 + 6 + 6 + 6
P = 24
Method Two:
You can also use multiplication to calculate the perimeter of a rhombus, since it has four equal sides.
P = 4 × 6
P = 24
As a result, the perimeter of the rhombus is 24 feet.
Find the Missing Lengths
Let us take an example to understand how we can find the missing lengths.
Example:
The perimeter of the square is 40 metres. Determine the length of a side of the square.
Solution:
All the sides of a square are equal in length.
4 × x = 40 Write an equation for the perimeter.
x = 10 Divide each side by 4.
As a result, the length of each side is 10 m.
Solved Perimeter Examples
Example 1:
What is the perimeter of the shape?
Solution:
Each grid is a unit square.
Count the units as you go around the figure.
There are 16 units around the figure.
As a result, the perimeter is 16 inches.
Example 2:
Determine the perimeter of the rectangle.
Solution:
Method One:
The perimeter is calculated by adding the lengths of the shape’s sides.
P = 6 + 9 + 6 + 9
P = 30
Method Two:
You can also use multiplication to find the perimeter of a rectangle as its opposite sides are equal.
P = 2 × 6 +2 × 9
P = 30
As a result, the perimeter of the rectangle is 30 cm.
Example 3:
Ken takes his daily morning walk around a playground. The playground is in the shape of a quadrilateral, with sides measuring “112” m, “85” m, “x” m, and “102” m in length. The perimeter is 340 m. Find the value of x.
Solution:
x + 85 + 112 + 102 = 340 Write an equation for the perimeter.
x + 299 = 340 Add the known side lengths.
x + 299 – 299 = 340 – 299 Subtract 299 from each side.
x = 41
Hence, the length of the unknown side or “x” is 41 m.
Example 4:
Your favorite chocolate bar is made up of 6 unit squares, with each side measuring 1 inch in length. Determine its perimeter.
Solution:
A unit square has its sides measuring 1 unit each.
We know that all the sides of each little square are equal to one.
We get 3 inches by counting and adding the sides of squares along the length of the bar.
The sides of the squares add up to 2 inches across the width of the bar.
As a result, the length of the bar is 3 inches and its width is 2 inches.
Use multiplication to find the perimeter of the bar of chocolate.
P = 2 × 3 +2 × 2
P= 10
As a result, the perimeter of the chocolate bar is 10 inches.
The lengths of the sides of an irregular shape differ. To find the perimeter of an irregular shape, add the lengths of all the sides together.
All the sides of a regular shape are equal. Multiply the number of sides by the length of each side to find the perimeter of a regular shape.