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Area and perimeter

Revise Area and perimeter for Mathematics D 4024 (O Level) — revision notes, 24 practice questions and instant AI marking.

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  Cambridge O Level Mathematics (Syllabus D) 4024

Area and perimeter

The big idea: Perimeter is a distance round the edge, measured in cm. Area is the space inside, measured in cm². Only the triangle formula is on the List of formulas, so the other three must be learnt.

Summary — What This Chapter Covers
  • Perimeter: add the lengths of all the sides.
  • Rectangle: area = length × width (memorise).
  • Triangle: area = ½ × base × perpendicular height (given on the List of formulas).
  • Parallelogram: area = base × perpendicular height (memorise).
  • Trapezium: area = ½(a + b)h, where a and b are the parallel sides (memorise).
  • Rearrange the formulas to find a missing length, including problems that lead to an equation.
1. Rectangles
Syllabus 5.2 · Paper 1 & 2

Area = length × width

Perimeter of a rectangle = 2 × (length + width). Area = length × width.

Worked Example

A rectangle has area 54 cm2 and length 9 cm. Find its width and its perimeter.

Practice Question 1

A rectangle has perimeter 34 cm and length 11 cm. Find its area.

2. Triangles
Syllabus 5.2 · Paper 1 & 2

Half base times perpendicular height

The height must be perpendicular to the base you choose. For an obtuse-angled triangle the height may fall outside the triangle.

Given on the List of formulas A = ½bh
Worked Example

(a) A triangle has base 12 cm and perpendicular height 7.5 cm. Find its area. (b) Another triangle has area 36 cm2 and base 9 cm. Find its perpendicular height.

3. Parallelograms
Syllabus 5.2 · Paper 1 & 2

Base × perpendicular height

Cut a triangle off one end of a parallelogram and move it to the other end: you get a rectangle with the same base and the same perpendicular height. The slanting side is used for the perimeter, never for the area.

Memorise Area of parallelogram = base × perpendicular height
Practice Question 2

A parallelogram has sides 10 cm and 6 cm. The perpendicular height onto the 10 cm side is 5 cm. Find its area and its perimeter.

4. Trapeziums
Syllabus 5.2 · Paper 1 & 2

Average of the parallel sides × height

Add the two parallel sides, halve, and multiply by the perpendicular distance between them.

Memorise Area of trapezium = ½(a + b)h    a and b parallel, h the perpendicular distance between them
Worked Example

A trapezium has parallel sides 7 cm and 13 cm, 6 cm apart. Find its area.

Practice Question 3

A trapezium has area 84 cm2 and parallel sides 9 cm and 15 cm. Find the distance between the parallel sides.

5. Problems Leading to Equations
Syllabus 5.2 · Paper 1 & 2

Let x be the length

Memorise
Rectangle

A = lw. P = 2(l + w).

Triangle

A = ½bh (given). h is perpendicular to b.

Parallelogram
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