# Area

## What is Area?

Area is the amount of space taken up by the total surface of a shape. It gives us a view of the amount of space inside the shape, rather than just around the outside edges.

## Understanding Area

Area is a useful measurement in math when we are working with shapes. We can find the area of many different two dimensional shapes:

- Rectangles
- Triangles
- Circles

Whenever we are looking at a shape, it is handy to remember that area is made up of all the space on the inside of the shape.

We can even find the area of complex shapes, like this one:

We just need to look for simple shapes inside the complex one, and work out the area for each one. In this case, we can find the area of the triangle as well as the square, then combine the two areas together to get a total.

Area of the square + Area of the triangle = Total Area

We measure area by counting up the units which are contained within the shape. To find the area of a shape, we need to know exactly how many units will fit inside it. There are two different ways to do this.

## Count the Units

The first is to count the units by adding up how many squares will fit into the shape, like this:

A handy way of practicing the concept of units in area is to cut out some card squares and see how many will fit inside a simple shape. Count the number of card squares to find the area.

Use the same card squares to test out the area of different shapes, like this:

Did you notice? Even when the shape changed, the total number of units was the same for the rectangle because the same number of units could fit inside it.

This is a great way of understanding that the area of a shape can be the same even for shapes with different dimensions.

This can work well for small, simple shapes but it gets tricky if the shape is very large or more complex.

## Use a Formula

Another way of working out area is to use a formula. A formula is an accurate way of calculating the area of a shape. To use a formula for area, you will need to know some key facts about the shape. You will also need to know the right formula for the shape.

The formula for a rectangular or square shape is LENGTH (l) × WIDTH (w). You need to know the length of the shape as well as the width of the shape to use a formula. Multiply these two numbers together, and you will have the area.

10 × 20 = 200 units^{2}

## Which Units Should I Use?

Area units are written as a numeral squared (raised to the power of 2). This means the answer must have a squared sign, like this:

When you are calculating area, the units you use will be the same for each side of the shape. If you know the sides are measured in feet, for example, then your answer will be written in feet squared. If you know the sides are measured in centimeters, your answer will be written in centimeters squared.

10 cm × 20 cm = 200 cm^{2}

There are also formulas for other simple two dimensional shapes. Memorizing these formulas helps you calculate area quickly and easily.

## Triangles

The formula for a triangle is:

base × height / 2

If you know the base of this triangle is 10 cm and the height is 10 cm, you can use the formula of base x height divided by 2, to find the area.

10 × 10 / 2

100 / 2

Area = 50 cm^{2} – Don’t forget! If you are calculating the area of a shape, the answer is always in units squared.

Did you know that the area of a triangle is half of area of the rectangle that could be made by doubling the triangle? like this:

Which is why the formula for the area of a triangle is essentially the same as the formula for the area of a rectangle divided by two.

## Circles

Circles can be tricky when it comes to area – laying out lots of square cards onto a circle and adding them all up is one way, but there is a far simpler idea that can help too! All you need to know is the length of the radius of the circle (from the mid point of the circle directly to the outside edge).

The use the formula 𝐴 = 𝜋𝑟^{2}

Measure the radius of the circle. Find the square of the radius. Multiply by 3.142 (the value of 𝜋 to find the area.) Remember to use the squared symbol for your answer!

- 𝐴 = 𝜋𝑟
^{2} - A = 3.142 × 5
^{2} - A = 3.142 × 25
- A = 78.55 feet
^{2}

## Why is Area Important to Learn?

Area helps us to understand the way that shapes work. By being able to calculate area, we can find out more about the two dimensional objects that we see around us every day. We can understand their dimensions and know how to work with them in everyday tasks.

Area is a great example of math which has real world application. If we are working with a two dimensional shape, there is a good chance that area will be a part of our thinking!

Area calculations help out with many everyday tasks, such as jobs around the house. They also help people at work too. Here are some examples of area being used in real life:

- Wall papering a wall in a bedroom
- Covering a book for school
- Lining a cake pan
- Buying material for curtains on a window
- Calculating the amount of paint needed for a fence
- Ordering the correct number of tiles for a bathroom wall
- Working out the land size of a property
- Giving a customer an accurate quote for mowing their lawn

Lots of people find that area is a great next step to master after they have learned about perimeter. Together, perimeter and area help us to understand and work with the shapes which are all around us.