MEASUREMENT OF AREAS AND VOLUMES..

 Example: Sam cuts grass at $0.10 per square meter

How much does Sam earn cutting this area:

 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

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

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

Circle 

Area = π × r² 
Circumference = 2 × π × r
r = radius

Ellipse
Area = πab

 Parallelogram
Area = b × h
b = base
h = vertical height

Rectangle
Area = w × h
w = widthh = height 

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

 Square
Area = a²
a = length of side

 Trapezoid (US)
Trapezium (UK)
Area = ½(a+b) × h
h = vertical height

Triangle
Area = ½ × b × h
b = baseh = vertical height 




Note: h is at right angles to b: