Area of Plane Shapes

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?

Area Count

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?

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