# What is Area?

*Area is the size of a surface!*

### Example:

These shapes all have the same area of 9:

## Area of Simple Shapes

There are special formulas for certain shapes:

### Example: What is the area of this rectangle?

The formula is:

Area = w × h

w = width

h = height

The width is 5, and the height is 3, so we know **w = 5** and **h = 3**. So:

Area = 5 × 3 = **15**

Read Area of Plane Shapes for more information.

## Area of Difficult Shapes

To help you understand an area, imagine painting it and how much paint you might use.

You can sometimes break a shape up into two or more simpler shapes:

### Example: What is the area of this Shape?

Let's break the area into two parts:

Part A is a square:

^{2}= 20m × 20m = 400m

^{2}

Part B is a triangle. Viewed sideways it has a base of 20m and a height of 14m.

^{2}

So the total area is:

^{2}+ 140m

^{2}= 540m

^{2}

## Area by Adding Up Triangles

You can also break up a shape into triangles:

Then measure the base (**b**) and height (**h**) of each triangle:

Then calculate each area (using Area = ½b × h) and add them all up.

## Area by CoordinatesIf you know the coordinates of each corner point you can use the method explained in Area of Irregular Polygons: There is an Area of a Polygon by Drawing Tool if you need it. |

## Area by Counting Squares

You can also put your shape on a grid and count the number of squares:

This rectangle has an area of **15**

If each square was **1 cm** on a side, then the area would be **15 cm ^{2}** (15 square cm)

Sometimes the squares may not match the shape exactly, so you will need to "approximate" an answer.

One way is:

- more than half a square counts as 1
- less than half a square counts as 0

Like this:

This pentagon has an area of **approximately 17**

Or just use your eyes and count a whole square when the areas seem to add up, like with this circle, where the area marked "**4**" seems equal to about 1 whole square (also for "**8**"):

This circle has an area of **approximately 14**