Question

Write the formulas of the following:
a) square
b)rectangle
c) triangle
d) circle​

Answer 1

Answer:

= base

h = vertical height square Square

Area = a2

a = length of side

rectangle Rectangle

Area = w × h

w = width

h = height parallelogram Parallelogram

Area = b × h

b = base

h = vertical height

trapezoid Trapezoid (US)

Trapezium (UK)

Area = ½(a+b) × h

h = vertical height circle Circle

Area = π × r2

Circumference = 2 × π × r

r = radius

ellipse Ellipse

Area = πab

sector Sector

Area = ½ × r2 × θ

r = radius

θ = angle in radians

Note: h is at right angles to b: altitude

Example: What is the area of this rectangle?

Area Count

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?

circle radius 3

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?

Triangle base=20, 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:

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