# What is Area?

*Area is the size of a surface!*

### Example:

These shapes all have the same area of 9:

It helps to imagine **how much paint** would cover the shape.

## 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**:

Area = 5 × 3 = **15**

Learn more at Area of Plane Shapes.

## Area by Counting Squares

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

The 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)

## Approximate Area by Counting Squares

Sometimes the squares don't match the shape exactly, but we can get an "approximate" 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 we can count one square when the **areas seem to add up**.

Example: Here the area marked "**4**" seems equal to about 1 whole square (also for "**8**"):

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

#### But using a formula (when possible) is best:

### Example: The circle has a radius of 2.1 meters:

The formula is:

Area = π × r^{2}

π = the number pi (3.1416...)

r = radius

The radius is **2.1m**, so:

Area = 3.1416... × (2.1m)^{2}

= 3.1416... × (2.1m × 2.1m)

= **13.8544... m ^{2}**

So the circle has an area of **13.85 square meters** (to 2 decimal places)

## Area of Difficult Shapes

We 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

We 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 Coordinates

When we know the coordinates of each corner point we can use the Area of Irregular Polygons method.

There is an Area of a Polygon by Drawing Tool that can help too.