Area of Plane Shapes

Area is the size of a surface! TriangleArea = ½ × b × hb = baseh = vertical height SquareArea = a2a = length of side RectangleArea = w × hw = widthh = height ParallelogramArea = b × hb = baseh = vertical height Trapezoid (US)Trapezium (UK)Area = ½(a+b) × hh = vertical height Circle Area = π × r2 Circumference = 2 × π × rr = radius EllipseArea = πab SectorArea = ½ × r2 × θ r = radiusθ = 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? 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:

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