Area & PerimeterCambridge IGCSE Maths: Revision notes

Section 1

What is perimeter?

The perimeter of a shape is the total distance around its outside edge, found by adding the lengths of all sides.

For a rectangle with length $l$ and width $w$ : perimeter $= 2l + 2w$ or $2(l+w)$ .

For irregular shapes, add every labelled side length — you may need to work out missing side lengths first using the shape's properties.

Key termsperimeter

Common mistake

Forgetting to include a missing side that must be calculated (not just read off) is a very common error in compound shape perimeter questions.

Section 2

How do I find the area of a rectangle, triangle, parallelogram and trapezium?

Shape	Formula	Given in exam?
Rectangle	$A = l \times w$	Not given
Triangle	$A = \frac{1}{2} \times \text{base} \times \text{height}$	Given
Parallelogram	$A = \text{base} \times \text{height}$	Not given
Trapezium	$A = \frac{1}{2}(a+b) \times h$	Not given

For a triangle, the height must be the perpendicular height, not a slanted side. For a trapezium, $a$ and $b$ are the two parallel sides.

Key termsbaseperpendicular height

Example

A trapezium has parallel sides 6 cm and 10 cm, and height 4 cm. Area = 0.5 × (6+10) × 4 = 32 cm².

Section 3

How do I find the perimeter and area of compound shapes?

A compound shape is made from two or more basic shapes joined together.

Method:

Split the compound shape into simple shapes (rectangles, triangles, etc.)
Work out any missing side lengths using the shape's overall dimensions
Find the area of each simple shape separately
Add the areas together for total area
For perimeter, add only the outer edges — internal dividing lines are not part of the perimeter

Key termscompound shape

Exam tip

Sketch the split shapes separately and label every side you calculate — examiners award method marks for clearly shown working.

Section 4

How do I convert between units of area?

Area units convert using the square of the linear conversion factor, since area has two dimensions.

$1 \text{ m} = 100 \text{ cm}$ , so $1 \text{ m}^2 = 100^2 = 10\,000 \text{ cm}^2$
$1 \text{ cm} = 10 \text{ mm}$ , so $1 \text{ cm}^2 = 10^2 = 100 \text{ mm}^2$
$1 \text{ km} = 1000 \text{ m}$ , so $1 \text{ km}^2 = 1000^2 = 1\,000\,000 \text{ m}^2$

To convert a larger unit to a smaller one, multiply; to convert smaller to larger, divide.

Key termsunit conversion

Common mistake

Using the linear conversion factor instead of squaring it is the single most common area-conversion error, e.g. writing 1 m² = 100 cm² instead of 10 000 cm².

Section 5

How do I find missing lengths in compound shape problems?

When a compound shape gives only some side lengths, use the fact that opposite sides of rectangular sections must match:

Identify which sides are 'shared' between two parts of the shape
Use addition or subtraction of known lengths to find the missing one
Label the newly found length on your diagram before continuing

Must Know

Perimeter = sum of all outer sides; area formulas: rectangle $lw$ , triangle $\frac{1}{2}bh$ , parallelogram $bh$ , trapezium $\frac{1}{2}(a+b)h$
Only the triangle area formula is given in the exam — memorise the others
Triangle height must be perpendicular to the base, not a slanted side
Compound shapes: split into simple shapes, find missing lengths, sum areas
Area units convert by squaring the linear conversion factor (e.g. 1 m² = 10 000 cm²)
Perimeter of a compound shape only includes outer edges, not internal dividing lines

That's the notes covered.

Carry on to the next subtopic.