Definition of Perimeter
| 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.
| 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.
| 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.
| 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.
| 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.
| 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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Nice emma really precise information.. I appreciate u
Hey Raptor! Thanks very much for the positive feedback, very much appreciated!
explains everything for a child or a confused student in their ap maths class who is lost in the more detailed mathematics
Draw all types of polygon and its area and perimeter class 7th NCERT course
I’m just curious if the area between the polygon and the circumscribed circle has a name.
https://www.superprof.co.uk/resources/academic/maths/geometry/plane/orthocenter-centroid-circumcenter-and-incenter-of-a-triangle.html
Draw all types of polygon and its area and perimeter