Area and perimeter
Perimeter is the distance around the outside of a shape; area is the space inside it. Four area formulas cover the straight-sided shapes on the papers, and compound shapes are built from them.
Part 1 of 3: Learn it
In short
- Triangle = ½ × base × perpendicular height; trapezium = ½(a + b)h.
- Split compound shapes into rectangles and triangles, or take a piece away from a bigger shape.
- 1 m² = 10 000 cm², because 1 m = 100 cm in both directions.
Where this is in your specification
Spec points: DfE G14, G16 and G17
| Board | Topic: Area, perimeter and volume |
|---|---|
| DfE content | G12, G13, G14, G16, G17, G18, N8 |
| AQA 8300 | Geometry and measures |
| Edexcel 1MA1 | Geometry and measures |
| OCR J560 | 10 Mensuration |
| Eduqas C300 | HG12, HG14, HG16 to HG18 |
| Cambridge IGCSE 0580 | E5.1 to E5.5 |
| National 5 C847 75 | Geometric skills: volumes of solids, arcs and sectors |
Area formulas
| Shape | Area |
|---|---|
| Rectangle | length × width |
| Triangle | ½ × base × height |
| Parallelogram | base × height |
| Trapezium | ½ × (a + b) × h, where a and b are the parallel sides |
The height is always perpendicular (at right angles) to the base. A sloping side is not the height.
Compound shapes
Split the shape into pieces you know, find any missing lengths from the lengths you are given, and add the areas. Sometimes it is quicker to find a big rectangle and subtract the missing corner.
Perimeter
Add up every outside edge. Go round the shape from one corner and tick each side as you add it, so none is missed or counted twice.
Area units
- 1 cm² = 100 mm² (10 × 10).
- 1 m² = 10 000 cm² (100 × 100).
- 1 km² = 1 000 000 m².
Find the area of a triangle with base 9 cm and height 7 cm.
Show the answer
½ × 9 × 7 = 31.5 cm².
Part 2 of 3: See it worked
Worked examples
Example 1
A trapezium has parallel sides of 7 cm and 13 cm and a perpendicular height of 6 cm. Find its area.
- a + b = 7 + 13 = 20
- ½ × 20 × 6
Answer: 60 cm².
Example 2
An L-shape is a 10 cm by 8 cm rectangle with a 4 cm by 3 cm rectangle cut from one corner. Find its area and perimeter.
- Area: 10 × 8 − 4 × 3 = 80 − 12 = 68 cm²
- Cutting a corner out moves two edges inwards but keeps their total length
- Perimeter = 2 × (10 + 8) = 36 cm
Answer: Area 68 cm², perimeter 36 cm.
Example 3
A field is 120 m by 45 m. One bag of seed covers 600 m². How many bags are needed?
- Area = 120 × 45 = 5400 m²
- 5400 ÷ 600 = 9
Answer: 9 bags.
Common mistakes
- Using the sloping side instead of the perpendicular height.
- Forgetting the ½ in the triangle or trapezium formula.
- Converting 1 m² to 100 cm². It is 10 000 cm².
- Giving area in cm instead of cm².
Find the area of a parallelogram with base 12 cm and perpendicular height 5 cm.
Show the answer
12 × 5 = 60 cm².
Part 3 of 3: Test yourself
Check yourself
Answer each one in your head or on paper first, then open it to check.
Find the area of a triangle with base 9 cm and height 7 cm.
½ × 9 × 7 = 31.5 cm².
Find the area of a parallelogram with base 12 cm and perpendicular height 5 cm.
12 × 5 = 60 cm².
Convert 3.5 m² to cm².
3.5 × 10 000 = 35 000 cm².
Jobs that use this
- Architect (öffnet einen neuen Tab)
- Quantity surveyor (öffnet einen neuen Tab)
- Land surveyor (öffnet einen neuen Tab)
Each link opens the job profile on the National Careers Service (England). In the rest of the UK: My World of Work (Scotland), Careers Wales, nidirect careers (Northern Ireland).
Diese Lernzettel sind auf Englisch, weil sie britischen Prüfungslehrplänen folgen.
Full lessons and marked practice for this course are coming soon to Brainlag Learn. See courses