# Area of Plane Shapes

*Area is the size of a surface!Learn more about Area, or try the Area Calculator.*

Triangle Area = ½ × b × h b = base h = vertical height | Square Area = a ^{2}a = length of side | |||

Rectangle Area = w × h w = width h = height | Parallelogram Area = b × h b = base h = vertical height | |||

Trapezoid (US) Trapezium (UK) Area = ½(a+b) × h h = vertical height | Circle Area = π × r ^{2} Circumference = 2 × π × r r = radius | |||

Ellipse Area = πab | Sector Area = ½ × r ^{2} × θ r = radius θ = angle in radians |

Note: h is at right angles to b: |

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

The formula is:

Area = w × h

w = width

h = height

We know **w = 5** and **h = 3**, so:

Area = 5 × 3 = **15**

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

Radius = r = 3

Area | = π × r^{2} | |

= π × 3^{2} | ||

= π × (3 × 3) | ||

= 3.14159... × 9 | ||

= 28.27 (to 2 decimal places) |

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

Height = h = 12

Base = b = 20

Area = ½ × b × h = ½ × 20 × 12 = **120**

A harder example:

### Example: Sam cuts grass at $0.10 per square meter

### How much does Sam earn cutting this area:

Let's break the area into two parts:

Part A is a square:

Area of A = a

^{2}= 20m × 20m = 400m^{2}Part B is a triangle. Viewed sideways it has a base of 20m and a height of 14m.

Area of B = ½b × h = ½ × 20m × 14m = 140m

^{2}So the total area is:

Area = Area of A + Area of B = 400m

^{2}+ 140m^{2}= 540m^{2}

Sam earns $0.10 per square meter

Sam earns = $0.10 × 540m

^{2}= $54