worldofcalcsArea Calculator
Area
50 cm²
Perimeter
30 cm
Working
A = l × b = 10 × 5 = 50
P = 2(l + b) = 2 × (10 + 5) = 30
What is area?
Area is the amount of flat surface a shape covers, measured in square units such as cm² or m². Perimeter is the distance around its edge. This calculator covers the shapes in the NCERT mensuration chapters, shows each formula with your numbers substituted, and can use π = 22/7 so the answers match your textbook.
Key area formulas
Rectangle = l × b · Triangle = ½ × b × h · Circle = πr² · Trapezium = ½(a + b)h · Heron's formula = √(s(s − a)(s − b)(s − c)), s = (a + b + c) ÷ 2
All lengths must be in the same unit, and the area comes out in that unit squared. The height of a triangle, parallelogram or trapezium is measured at right angles to the base.
Tips for mensuration problems
- Convert all measurements to one unit before calculating: 1 m = 100 cm, so 1 m² = 10,000 cm².
- π = 22/7 gives neat answers when the radius is a multiple of 7. Otherwise use 3.14, unless the question says which value to use.
- Use Heron's formula when you know all three sides but not the height.
- A rhombus's diagonals bisect each other at right angles, so each side is √((d₁/2)² + (d₂/2)²).
- For a field or plot, the land area converter turns square feet into gaj, bigha or acres.
Worked example: Heron's formula
- A triangle has sides 13 cm, 14 cm and 15 cm
- Semi-perimeter s = (13 + 14 + 15) ÷ 2 = 21
- s − a = 8, s − b = 7, s − c = 6
- Area = √(21 × 8 × 7 × 6) = √7,056 = 84 cm²
- Perimeter = 13 + 14 + 15 = 42 cm
Area and perimeter formulas
The formulas used for each shape.
| Shape | Area | Perimeter |
|---|---|---|
| Square | a² | 4a |
| Rectangle | l × b | 2(l + b) |
| Triangle (base and height) | ½ × b × h | a + b + c |
| Triangle (three sides) | √(s(s − a)(s − b)(s − c)) | a + b + c |
| Circle | πr² | 2πr |
| Parallelogram | b × h | 2(a + b) |
| Trapezium | ½(a + b) × h | a + b + c + d |
| Rhombus | ½ × d₁ × d₂ | 4a |
π ≈ 3.1416 or 22/7.