Area is calculated when we want to find the flat surface to:

• collect sunshine for solar panels
• paint a wall
• tile a bathroom
• carpet a floor
• spread grass seeds to grow a lawn
• fertilize a garden

A Quadrilateral is a four-sided shape such as a rectangle, a square, a parallelogram and a trapezoid.

The area rules for each of these is based on the Area of Rectangle rule and are:

Area of Rectangle = L × W

Area of Square = S × S

Area of Parallelogram = L × H

 Area of Trapezoid = (A + B) × H 2

CONVERTING AREA UNITS

To change:

• square centimetres (cm2) to square millimetres (mm2), multiply by 10 and then multiply again by 10 (or multiply by 100).
• square metres (m2) to square millimetres (mm2), multiply by 1000 and by 1000 again (or multiply by 1 000 000).
• square metres (m2) to square centimetres (cm2), multiply by 100 and by 100 again (or multiply by 10 000).
• square kilometres (km2) to square metres (m2), multiply by 1000 and by 1000 again (or multiply by 1 000 000).

IF YOU SQUARE THE NAME, YOU SQUARE THE NUMBER.

Example One - Area of Rectangle The International Space Station has been continuously occupied by astronauts performing experiments in astronomy, biology, chemistry and physics for over 12 years. It has four double-sided photo-voltaic arrays (solar panels) to make electricity. Each of the 8 panels measures 58 metres long by 3 metres wide. What is its total sunlight collection area?

Area of Rectangle
= L × W
= 58 × 3
= 174 square metres or 174 m2

Area of 8 Rectangular Panels
= 174 × 8
= 1392 square metres or 1392 m2

Did You Know That...? The commonly used world map is misleading when displaying the actual area of countries. The Gall-Peters Map Projection shown above is more accurate.

Example Two - Area of Square What is the tiled area of a square bathroom floor with a side of 3000mm?
(Remember carpenters measure accurately in millimetres, but tiles are priced by the square metre.)

Area of Square
= S × S
= 3 × 3
= 9 m2

Example Three - Area of Parallelogram

One thousand postage stamps in the shape of a parallelogram are printed. Each stamp has a length of 25 mm and a perpendicular height (at right angles to the length) of 12 mm. What is the area of glue (on the reverse side) to cover 1000 stamps? Area of Parallelogram
= L × H
= 25 × 12
= 300 mm2

Area of glue on 1000 stamps
= 300 × 1000
= 300 000 mm2 or 3000 cm2

Example Four - Area of Trapezoid

A farm in the shape of a trapezoid and has parallel sides of 1000 metres and 2000 metres respectively. The perpendicular height is 500 metres. What is the area (in hectares) of this property? (Hint: 1 hectare = 10 000 square metres) Area of Trapezoid = (A + B) × H 2
 = (1000 + 2000) × 500 2

= 1500 × 500
= 750 000 m2
= 75 hectares

Example Five - Painting a Wall

Calculate the quantity of paint required to paint a rectangular bedroom wall 4 metres by 2.4 metres. Two coats of paint are needed. One litre of paint covers 10m2.

Area (1 coat)
= L × W
= 4 × 2.4
= 9.6 m2

Area (2 coats)
= 9.6 × 2
= 19.2 m2

Number of litres
= 19.2 / 10
= 1.92
= 2 litres (Remember that you can't buy parts of litres of paint from the hardware store.)

Questions

Find the areas of the following quadrilaterals. Be careful to convert the dimensions to the same units first.

Q1. Square with a side of 7 metres
Q2. Rectangle with a length of 10km and a width of 700 metres
Q3. Parallelogram with a length of 5 metres and a perpendicular height of 60cm
Q4. Trapezoid with parallel sides of 10cm and 6cm, and a perpendicular height of 5cm

A1. 49 m2
A2. 21.4 km2 or 7000000 m2
A3. 3 m2 or 30000 cm2
A4. 5 cm2

Maths Fun - Trapezoidal Numbers

Trapezoidal Numbers (also called Polite Numbers) are the sum of consecutive positive integers. Examples of Trapezoidal Numbers are:

• 1 + 2 = 3
• 1 + 2 + 3 = 6
• 2 + 3 + 4 = 9
• 3 + 4 + 5 + 6 = 18
• 10 + 11 + 12 + 13 = 46

Why is the number 4 "impolite"? Why do you think these are called "Trapezoidal"? (Hint: Think of arranging blocks like steps.)