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 = a2 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 × r2 Circumference = 2 × π × r r = radius
	Ellipse Area = πab			Sector Area = ½ × r2 × 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 × r2
		= π × 32
		= 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 = a² = 20m × 20m = 400m²

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 = 140m²

So the total area is:

Area = Area of A + Area of B = 400m² + 140m² = 540m²

Sam earns $0.10 per square meter

Sam earns = $0.10 × 540m² = $54