19.1 Perimeter and area of 2D shapes — Learn

Prerequisites: identify lengths and right angles; multiply whole numbers and decimals.

Objectives: calculate perimeters and areas of rectangles, triangles, parallelograms and trapezia; find missing lengths from area.

Perimeter and area

Perimeter is the distance around a flat shape. Add every outside side. Area measures the surface covered, so use square units.

For a rectangle, $P=2l+2w$ and $A=lw$. For a triangle, $A=\frac12 bh$, where $h$ meets the base at a right angle. A parallelogram uses $A=bh$. A trapezium uses the average of its parallel sides times its perpendicular height.

Example 1. A rectangle is 8 cm long and 3 cm wide. Work out its perimeter and area.

Add the four outside sides: $8+3+8+3=22$.

Multiply length by width: $8\times3=24$.

So the perimeter is $22\text{ cm}$ and the area is $24\text{ cm}^2$.

Example 2. A trapezium has parallel sides 7 cm and 13 cm, and height 5 cm. Work out its area.

Average the parallel sides: $\frac{7+13}{2}=10$.

Multiply by the perpendicular height: $10\times5=50$.

So the area is $50\text{ cm}^2$.

Example 3. A parallelogram has base 9 cm and perpendicular height 4 cm. Work out its area.

Multiply base by perpendicular height: $9\times4=36$.

So its area is $36\text{ cm}^2$.

Example 4. A triangle has base 9 m and area $36\text{ m}^2$. Work out its perpendicular height.

Double the area: $2\times36=72$.

Divide by the base: $72\div9=8$.

So its height is $8\text{ m}$.

Watch out. Perimeter uses length units, while area uses square units. Check the unit after each calculation.

At the first progress check, compare a rectangle and triangle with the same base and height. Which has more area, and by how much?

Progress check

A rectangular lawn beside the pond is $12$ m by $9$ m. Work out its perimeter and its area. State the unit for each answer.

You should now be able to

• add the outside side lengths to find perimeter;
• use the correct area formula for rectangles, triangles, parallelograms and trapezia;
• use area to find an unknown perpendicular height;
• write length units for perimeter and square units for area.