Area and Perimeter Calculator

Choose a shape, enter its measurements and get the area and the perimeter together, with the formula and every step of the working — the way your NCERT textbook writes it. Works in mm, cm, m, km, inches, feet and yards, and shows the area in other square units too.

Shape

Unit of length

Length (l)

Breadth (b)

Area

60 cm²

Perimeter

34 cm

Formulas: Area = l × b · Perimeter = 2(l + b)

Area in other units: 0.006 m² · 0.0646 ft² · 9.3 in²

Step-by-step solution

Area = l × b = 12 × 5 = 60 cm²
Perimeter = 2(l + b) = 2 × (12 + 5) = 2 × 17 = 34 cm

How to use the area calculator

Pick the shape: square, rectangle, triangle (base & height or three sides), circle, parallelogram, trapezium or rhombus.
Choose the unit and type the measurements. Optional sides are only needed for the perimeter.
For a circle, choose π exactly, 22/7 or 3.14 to match your textbook.
Read the area, perimeter, formulas and the step-by-step working.

Formulas

Square	`Area = a², Perimeter = 4a`
Rectangle	`Area = l × b, Perimeter = 2(l + b)`
Triangle	`Area = ½ × b × h, Perimeter = a + b + c`
Triangle (Heron)	`Area = √[s(s − a)(s − b)(s − c)], s = (a + b + c) ÷ 2` NCERT Class 9 — use when all three sides are known.
Circle	`Area = πr², Circumference = 2πr`
Parallelogram	`Area = b × h, Perimeter = 2(b + s)`
Trapezium	`Area = ½ × (a + b) × h`
Rhombus	`Area = ½ × d₁ × d₂, side = √[(d₁/2)² + (d₂/2)²]`

Solved examples

Example 1: Find the area and perimeter of a rectangle 12 cm long and 5 cm wide.

Area = l × b = 12 × 5 = 60 cm²
Perimeter = 2(l + b) = 2 × 17 = 34 cm

Answer: 60 cm² and 34 cm

Example 2: Find the area of a circle of radius 7 cm (π = 22/7).

Area = πr² = 22/7 × 7 × 7
= 22 × 7 = 154

Answer: 154 cm²

Example 3: Find the area of a triangle with sides 13 m, 14 m and 15 m.

s = (13 + 14 + 15) ÷ 2 = 21
Area = √[21 × 8 × 7 × 6] = √7056
= 84

Answer: 84 m²

Example 4: The diagonals of a rhombus are 6 cm and 8 cm. Find its area and perimeter.

Area = ½ × 6 × 8 = 24 cm²
Side = √(3² + 4²) = 5 cm
Perimeter = 4 × 5 = 20 cm

Answer: 24 cm² and 20 cm

Area vs perimeter

Perimeter is the length of the boundary — the fence around a field, the lace around a tablecloth — so it is measured in cm, m or km. Area is the surface inside the boundary — the carpet on a floor, the paint on a wall — so it is measured in square units such as cm² or m².

Two shapes can have the same perimeter but different areas: a 6 cm × 4 cm rectangle and a 5 cm × 5 cm square both have a 20 cm perimeter, but the square has the larger area (25 cm² vs 24 cm²).

Common mistakes in exams

Use the perpendicular height, not the slant side, for triangles, parallelograms and trapeziums. Convert every length to the same unit before multiplying, and remember that 1 m² = 10,000 cm², not 100 cm². When the question says "take π = 22/7", choose 22/7 here so your answer matches the answer key.

🎯 Asked in competitive exams

This topic regularly appears in the quantitative aptitude section of:

SSC CGL & CHSL
RRB NTPC & Group D
IBPS Clerk
Campus placement aptitude tests

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Frequently asked questions

What is the formula for the area of a triangle?

Area = ½ × base × height. If you know all three sides instead, use Heron’s formula: Area = √[s(s − a)(s − b)(s − c)], where s is half the perimeter.

How do I find the area of a circle?

Area = πr², where r is the radius. For radius 7 cm with π = 22/7, area = 22/7 × 49 = 154 cm². The circumference (perimeter) is 2πr = 44 cm.

What is the area of a trapezium?

Area = ½ × (sum of the parallel sides) × height. For parallel sides 8 m and 12 m and height 5 m, area = ½ × 20 × 5 = 50 m².

How do I find the perimeter of a rhombus from its diagonals?

The diagonals bisect each other at right angles, so each side = √[(d₁/2)² + (d₂/2)²]. Multiply by 4 for the perimeter.

Why can’t the calculator give the perimeter of a triangle from base and height?

Many different triangles share the same base and height, and their other two sides differ. Enter the two other sides (or use the three-sides option) to get the perimeter.

How do I convert m² to cm² or ft²?

1 m² = 10,000 cm² = 10.764 ft². The result box shows the area in other square units automatically.