METRONMETHOD. REASON. LEARN.
Measurement · 12 min

Area

Paint, carpet and tiles are sold to cover surfaces. Area tells you how much surface needs covering.

01Why this matters

Paint, carpet and tiles are sold to cover surfaces. Area tells you how much surface needs covering.

02See it

6 m4 m
The shaded triangle occupies half of a 6 m by 4 m rectangle. Its perpendicular height is 4 m. Diagram is schematic.
base 6 mheight 4 mrectangle 24 m²triangle 12 m²
Read left to right: base 6 m → height 4 m → rectangle 24 m² → triangle 12 m². Each panel connects one part of the example.

03Understand it

Area measures the amount of surface inside a two-dimensional boundary, in square units.

A rectangle of length l and width w contains l × w unit squares. A triangle with the same base and perpendicular height occupies half the area of the corresponding rectangle. Height must be measured at right angles to the base, not along a sloping edge.

04Guided example

Find the area of a triangular panel with base 6 m and perpendicular height 4 m.

  1. The matching rectangle has area 6 × 4 = 24 m².
  2. The triangle occupies half that rectangle: 24 ÷ 2 = 12.
  3. The area is 12 m². Each unit square is 1 m by 1 m.

05Try it

Find the area of a 7 m by 3 m rectangle.
A little hint

Multiply length by width.

06Practise it

Triangle base 8 cm, perpendicular height 5 cm. Area?
A little hint

Multiply base by height, then halve.

Square side 6 m. Area?
A little hint

Multiply the side by itself.

07Use it in the real world

A 5 m by 4 m floor covers 20 m². At 10 tiles per square metre it needs 200 tiles before allowing for cuts and breakage.

Go a little deeper

Area scales with the square of the length factor. Doubling every side of a shape multiplies its area by four, not two.

08Quick check

Rectangle area 24 m², length 8 m. Width?
A little hint

Divide area by length.

09Summary

Area measures the amount of surface inside a two-dimensional boundary, in square units. The area is 12 m². Each unit square is 1 m by 1 m.

Before moving on, explain the worked example in your own words. Use the hint on any question you want to revisit.

10Key idea

A = lw; triangle A = bh/2

A is area in m²; l, w, b (base) and h (perpendicular height) are in m.

rectangle w = A/l; triangle h = 2A/b

Find this in the formula library →