Area & Perimeter (Edexcel IGCSE Maths): Revision notes

Section 1

How do you find the perimeter of a shape?

The perimeter is the total distance around the outside of a 2D shape. To find it, add up the lengths of all the sides.

For a rectangle with length $l$ and width $w$ :

$P = 2l + 2w = 2(l + w)$

For any polygon, just sum every side length. Make sure every side is in the same units before adding, and watch for missing sides in compound shapes — you often need to work them out from the given lengths first.

Key termsPerimeter

Common mistake

Do not confuse perimeter with area. Perimeter uses addition of lengths (units: cm, m); area uses multiplication (units: cm(^2), m(^2)).

Exam tip

In compound shapes, redraw missing sides using the fact that opposite sides of a rectangle are equal — this fills in gaps before you add everything up.

Section 2

What is the area of a rectangle and a triangle?

Area measures the amount of surface a shape covers, measured in square units.

Rectangle: $A = l \times w$

Triangle: $A = \frac{1}{2} \times \text{base} \times \text{height}$

The height of a triangle must be the perpendicular height — the straight-line distance from the base to the opposite vertex, measured at a right angle to the base. This is not always the same as one of the sloping sides.

Key termsAreaPerpendicular height

Common mistake

In a triangle, using the slanted side as the height instead of the perpendicular height gives the wrong area — always check the right-angle mark in the diagram.

Example

A triangle with base 8 cm and perpendicular height 5 cm has area $\frac{1}{2} \times 8 \times 5 = 20\ \text{cm}^2$ .

Section 3

How do you find the area of a parallelogram and a trapezium?

Parallelogram: area is base times perpendicular height, just like a rectangle: $A = b \times h$

Trapezium: area is the average of the two parallel sides, multiplied by the perpendicular height between them: $A = \frac{1}{2}(a + b)h$

where $a$ and $b$ are the lengths of the two parallel sides and $h$ is the perpendicular distance between them.

Key termsParallelogramTrapezium

Think of it like this

Think of a trapezium as a rectangle with the excess triangle 'squashed' off one end — averaging the two parallel sides accounts for that slant.

Exam tip

Always identify which two sides are parallel in a trapezium before substituting into the formula — they are $a$ and $b$ , not just any two sides.

Section 4

How do you tackle compound shapes?

A compound shape is made from two or more basic shapes (rectangles, triangles, trapeziums) joined together. To find its area:

Split the shape into simple shapes you know formulas for.
Work out any missing lengths using the given measurements.
Find the area of each simple shape separately.
Add the areas together (or subtract, if one shape is cut out of another).

For perimeter of a compound shape, trace the outer boundary only — do not include internal lines used to split the shape into pieces.

Key termsCompound shape

Common mistake

Adding the internal dividing line into the perimeter is a very common error — the perimeter only counts the outer boundary.

Exam tip

Label each missing side with a letter and use addition/subtraction of known lengths before calculating any area — this avoids guessing.

Section 5

Worked example: area and perimeter of an L-shape

An L-shaped garden is made from a large rectangle $10\text{ m} \times 6\text{ m}$ with a smaller rectangle $4\text{ m} \times 3\text{ m}$ cut from one corner.

Area: $A = (10 \times 6) - (4 \times 3) = 60 - 12 = 48\ \text{m}^2$

Perimeter: trace the outer edge, working out the two missing sides ( $10 - 4 = 6\text{ m}$ and $6 - 3 = 3\text{ m}$ ): $P = 10 + 6 + 4 + 3 + 6 + 3 = 32\ \text{m}$

Always sketch the shape and label every side before calculating.

Example

Subtracting a cut-out rectangle's area from the whole rectangle is the standard method for L-shapes and similar compound shapes.

Must Know

Rectangle: $A = l \times w$ , $P = 2(l+w)$
Triangle: $A = \frac{1}{2} \times \text{base} \times \text{perpendicular height}$
Parallelogram: $A = \text{base} \times \text{perpendicular height}$
Trapezium: $A = \frac{1}{2}(a+b)h$ , where $a, b$ are the parallel sides
Compound shape area: split, calculate separately, then add or subtract
Compound shape perimeter: trace only the outer boundary, never internal split lines

That's the notes covered.

Carry on to the next subtopic.