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
r = radius

Ellipse
Area = πab

Sector
Area = ½ × r² × θ
r = radius
θ = angle in radians

Note: h is at right angles to b

Area Rectangle

The formula is:

Area = w × h
w = width
h = height

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

Area = 5 × 3 = 15

circle radius 3

Radius = r = 3

Triangle base=20, height=12

Height = h = 12

Base = b = 20

Area = ½ × b × h = ½ × 20 × 12 = 120

A harder example:

area grass

Let's break the area into two parts:

area grass in 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

1754, 1755, 1756, 1757, 1758, 1759, 1760, 1761, 3250, 3251