AREA OF PLANE FIGURES

Triangle

The area is the size of a surface.

Area = ½ × b × h

b = base

h = vertical height

Rectangle

Area = w × h

w = width

h = height

Trapezoid (US)

Trapezium (UK)

Area = ½(a+b) × h

h = vertical height

Ellipse

Area = πab

Square

Area = a2

a = length of side

 Parallelogram

Area = b × h

b = base

h = vertical height

Circle

Area = π × r2

Circumference = 2 × π × r

r = radius

Sector

Area = ½ × r2 × θ

r = radius

θ = angle in radians

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

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