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Definition of Perimeter

The perimeter in math is a vital concept. Take a look at the definition below.

Definition Two-Dimensional Shape Notation
Perimeter The distance around a shape that has two dimensions A shape that has two dimensions: length and width P

Take a look at a few examples of two-dimensional shapes below.

 

polygons_shapes

 

A B C
Square Polygon Circle

Sometimes, the perimeter of a specific shape has a special name. For example, the perimeter of a circle is referred to as the circumference. Below are some examples of where knowing the perimeter might be useful.

Shopping Finding the perimeter of a phone to buy a phone case
Construction Finding the perimeter of a fence
Home Finding the perimeter of a room to buy and install carpet

Perimeter of a Square

Let’s go through an example of a perimeter by starting with a simple shape: a square. The definition of a square is below.

Property 1 Property 2 Property 3
Square Has four sides and four corners The angles formed by these four corners are all 90 degrees All sides are equal length

As you can see, squares are special because all of their sides are of equal length. In order to find the perimeter, you simply add up the length of all of these sides.

square_dimensions

 

Formula 1 Formula 2
Perimeter of Square P = l+l+w+w P = 4*l

In maths, you will usually see the following notation:

Width
Length

Definition of Area

Now that you understand what the perimeter is, let’s take a look at the definition of an area.

Definition Notation
Area The size of the surface taken up by a two or three dimensional shape A

While the perimeter can help you understand the distance around an object, knowing the area can unlock a world of possibilities. Let’s take a look at some examples.

 

area_shapes

 

A B C
A = 1 A = 4 A = 4

The area of the different shapes depend highly on the boundaries of that shape, not the actual shape. For example, while the shape of B and C look completely different, they hold the same amount of squares.

Area of a Square

Let’s go through an example of an area using a square as our example again. When we talk about the area of a shape, we want to know how many units we can fit into the boundary of that shape.

Definition Measure
Area How many units can we fit into this shape Square units

We use square units because it is the standard measure for every measure. Square units are exactly as you saw in the last section: squares whose sides are equal to 1.

 

square_same_sides

Formula
Area of a Square A = l*l

The area of a square is just the length of the side times the length of the side. Take a look at a few examples.

 

square_areas

A B C
A = 1*1 = 1 A = 2*2 = 4 A = 3*3 = 9

 

Perimeter of Triangles

Triangles are shapes that have three sides and three interior angles. These interior angles have to add up to 180 degrees. There are three major types of triangles. Each type of triangle has their own perimeter formula.

Equilateral Three equal sides P = 3s
Isosceles Two equal sides P = 2s+b
Scalene No equal sides P = a+b+c

Perimeter of Rectangle

Triangles are shapes that have four sides and four right angles. They also have two pairs of sides that are the same length. This makes the perimeter easy to find.

Length
Width
Perimeter P = 2l + 2w

Perimeter of a Circle

A circle is a shape that is in the shape of an “o” letter. It has a centre point and each point on the line is equidistant to the centre point. Equidistant means the same distance.

radius
diameter
Circumference
Area \[A = \pi*r^{2}\]

Perimeters of Common Shapes

Other common shapes include: rhombus, rhomboid, trapezium, and regular polygon. Finding the perimeter of these is easy.

Rhombus P = 4s = length of side
Rhomboid P = 2(b+s) = length of base
Trapezium P = a+b+c+d Each side is a different length
Regular Polygon P = n*s = number of sides

Area of a Triangle

In order to find the area of a triangle, you need to know the height of the triangle and the length of the base. If you don’t know the height of the triangle, you can use Pythagorean theorem.

\[ A = \frac{1}{2}*b*h \]

Area of a Rectangle

Finding the area of a rectangle is quite easy. In order to find the area of a rectangle, you simply need to know the length and the width of the rectangle. Take a look at the formula below.

\[

A = l*w

\]

Area of a Circle

Finding the area of a circle is easy because you can actually do it three different ways.

1
2
3

Areas of Shapes Inside a Circle

In order for two circles two be concentric, they need to:

  • Share the same centre point
  • Be on the same plane
  • Not have the same radius

The area between two concentric circles is:

\[

A = \pi*(R^{2}-r^{2})

\]

Where R is the radius of the bigger circle.

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Emma

Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.