Chapters
Perimeter of a Shape
| Definition | Notation | |
| Perimeter | The distance around a shape |  |
A two dimensional shape is any shape that has two dimensions. These two dimensions are typically a length dimension and a width dimension. Take a look at some examples of two-dimensional shapes below.
| A | B | C |
| Circle | Sector | Ellipse |
Because the perimeter is found by measuring the distance around a shape, most shapes have their own distinct perimeter formula. However, sometimes you encounter shapes with no formula. Take a look below.
Area of a Shape
Now that you understand what a perimeter is, let’s take a look at what the area of a shape is. The definition and notation of the area of a shape can be found in the table below.
| Definition | Units | Notation | |
| Area | The space taken up by a shape | Square units |  |
As you can see, we typically measure the area of objects in square units. Square units are the basic unit for all areas. In this way, we can compare the area of any shape because they have the same units.
A square unit is simply a square with the length of 1 unit. Take a look below.
| A | B | C |
| 1 square unit | 2 square units | 4 square units |
Example of an Area
Like the perimeter of a shape, the formula for the area of a shape is specific to that shape. However, unlike the perimeter, the area of a shape is not dependent on the shape of an object.
| Perimeter | Area |
| Depends on the shape of the object | Doesn’t depend on the shape of the object |
In other words, while a shape may appear to be bigger than another, it doesn’t mean it’s area will be bigger. This sounds a little confusing, so let’s take a look at an example.
| A | B | |
| Perimeter |  |  |
| Area |  | |
Looking at the example above, the shape on the right, shape B, takes up more space. This is clear, as it’s perimeter is bigger. However, both shapes have the exact same area: 4 square units.
Again, this is because the perimeter depends highly on the actual shape of the object while the area only depends on what can be contained inside.
Uses of Area
While the concept of area can seem quite simple, it is extremely helpful in many different ways. You’d be surprised how often you use area in your own life! Let’s take a look at some practical examples of areas in real life.
| Capacity | Finding the area of a room to know how many people it can fit |
| Construction | Finding the area of construction area to build a park |
| Decoration | Finding the area to decorate a mood board |
Area of a Square
A square is classified as a quadrilateral. A quadrilateral is a polygon with four sides. A square is also a parallelogram, which is a special type of quadrilateral where opposite sides are parallel.
Squares have four right angles and have four sides that are all the same length. This makes finding the area easy:
\[
A = s^{2}
\]
Area of a Rectangle
A rectangle is also classified as a quadrilateral. In addition, a rectangle is also classified as a parallelogram.
Rectangles have four right angles and has two pairs of sides that are the same length. This makes finding the area easy.
\[
A = l*w
\]
Area of a Parallelogram
There are three major types of parallelograms. Here is how to find their areas:
| Rectangle |  |
| Square |  |
| Rhombus | First find the height. If it’s not given, use Pythagorean theorem. Then it’s  |
Area of a Trapezium
A trapezium, also known as a trapezoid, is a quadrilateral that only has one pair of sides that are parallel. In order to find the area of a trapezoid, you have to know the height and the length of both bases.
\[
A = \frac{1}{2}*h*(b_{1}+b_{2})
\]
Area of a Circle
A circle is a shape that is shaped like an “o”. Every point on the line of a circle is equidistant, meaning that it is the same distance, to the centre point. The radius is the distance from the centre point to the line while the diameter is the distance from end to end through the centre point.
The area of a circle is:
\[
A = \pi*r^{2}
\]
Area of a Sector
A circle sector is the area between two radii and the arc they form. You can find the area with this formula.
\[
A = \frac{\theta}{360} * \pi * r^{2}
\]
Area Between Two Concentric Circles
Concentric circles are circles that are on the same plane and share the same centre point. Here is the area formula.
\[
A = \pi(R^{2} - r^{2})
\]
Area of an Ellipse
An ellipse is shaped like an oval. It has a centre point, where it is cut in half at its longest part by the vertex. Here is the area formula.
\[
A = \pi*(semi-major axis)*(semi-minor axis) = \pi*a*b
\]
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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