Area & Perimeter
Formulas for rectangles, triangles, circles and composite shapes
Perimeter
Perimeter is the total distance around the outside of a shape. Add all side lengths.
| Shape | Perimeter Formula |
|---|---|
| Rectangle | P = 2(l + w) |
| Square | P = 4s |
| Triangle | P = a + b + c |
| Circle (circumference) | C = 2πr = πd |
Area Formulas
| Shape | Area Formula |
|---|---|
| Rectangle | A = l × w |
| Square | A = s² |
| Triangle | A = ½ × base × height |
| Parallelogram | A = base × height |
| Trapezium | A = ½(a + b) × h |
| Circle | A = πr² |
Use π ≈ 3.14 or 22/7, unless the question specifies otherwise.
Composite Shapes
Break the shape into simpler parts, find each area, then add or subtract.
Example: An L-shaped room. Split into two rectangles → find each area → add together.
Working Backwards & Key Tips
If area is given and one dimension is unknown, rearrange the formula.
Example: Rectangle has area 48 cm² and length 8 cm. Find width.
w = 48 ÷ 8 = 6 cm
Key Tips
- Area is always in square units (cm², m², km²)
- The height in a triangle is the perpendicular height, not the slant side
- For circles, be clear whether you need radius or diameter
- Remember C = πd — useful when you know the diameter directly
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What is the area of a square of side 5 cm?
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Answer: 25 cm²
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A circle has diameter 10 cm. What is its circumference? (Use π ≈ 3.14)
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Answer: 31.4 cm
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What is the perimeter of a regular hexagon with side 5 cm?
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Answer: 30 cm
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A rectangle has area 48 cm² and width 6 cm. What is its length?
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Answer: 8 cm
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