Area of Plane Shapes

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

Triangle with base b and vertical height h
Triangle
Area = ½ × b × h
b = base
h = vertical height
Square with side length a
Square
Area = a2
a = length of side
Rectangle with width w and height h
Rectangle
Area = w × h
w = width
h = height
Parallelogram with base b and vertical height h
Parallelogram
Area = b × h
b = base
h = vertical height
Trapezoid with parallel sides a and b, and vertical height h
Trapezoid (US)
Trapezium (UK)
Area = ½(a+b) × h
h = vertical height
Circle with radius r
Circle
Area = πr2
r = radius
Ellipse with semi-major axis a and semi-minor axis b
Ellipse
Area = πab
Sector of a circle with radius r and angle theta
Sector
Area = ½ × r2 × θ
r = radius
θ = angle in radians
Right angle showing altitude h is perpendicular to base b
Note: h is at right angles to b

Example: What's the area of this rectangle?

Rectangle with width 5 and height 3

The formula is:

Area = w × h
w = width
h = height

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

Area = 5 × 3 = 15

Example: What's the area of this circle?

Circle with radius 3

Radius = r = 3

Area   = π × r2
    = π × 32
    = π × (3 × 3)
    = 3.14159... × 9
    = 28.27 (to 2 decimal places)

Example: What's the area of this triangle?

Triangle with base 20 and height 12

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:

L-shaped grass lawn with dimensions

Let's break the area into two parts:

L-shaped grass lawn split into square A and triangle B

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
1754, 1755, 1756, 1757, 1758, 1759, 1760, 1761, 3250, 3251
Area Calculation Tool Area Area of Irregular Polygons Geometry Index