Area and Perimeter
8 min read · Updated September 26, 2026 · by the SolveCalcPro editorial team
Perimeter is the distance around a shape, measured in ordinary units such as metres. Area is the amount of surface inside it, measured in square units such as square metres. Together they answer everyday questions: how much fencing do I need, and how much paint?
Formulas
| Shape | Area | Perimeter |
|---|---|---|
| Rectangle | l × w | 2(l + w) |
| Square | s² | 4s |
| Triangle | ½ × b × h | a + b + c |
| Parallelogram | b × h | 2(a + b) |
| Trapezoid | ½(a + b) × h | sum of sides |
| Circle | πr² | 2πr |
Worked examples
- Rectangle 8 × 5: area 40, perimeter 26.
- Triangle with base 10 and height 6: area 30.
- Parallelogram with base 9 and height 4: area 36.
- Trapezoid with parallel sides 6 and 10 and height 4: area ½(16)(4) = 32.
- Circle with radius 7: area 49π ≈ 153.94 and circumference 14π ≈ 43.98.
Check any of them with the geometry calculator or the circle calculator.
Composite shapes
Split an irregular shape into simple ones, or subtract a piece from a bigger shape. An L-shaped room made from a 10 × 8 rectangle with a 4 × 3 corner removed has area 80 − 12 = 68.
A practical example
A garden 12 m by 9 m needs fencing of 2(12 + 9) = 42 m and has an area of 108 m². If a bag of seed covers 27 m², you need 4 bags.
Converting square units
Square units convert by squaring the length factor. 1 m = 100 cm, so 1 m² = 100 × 100 = 10,000 cm². Similarly 1 km² = 1,000,000 m². Use the unit converter for others.
Practice questions
Test yourself, then tap to check. Answers are calculated by the tools linked below.
- Area of a circle with radius 7.
Show answer
Area: 153.93804
- A circle has diameter 14. Find its area and circumference.
Show answer
Radius: 7 · Diameter: 14 · Circumference: 43.98229715
- How many kilometres is a 26.2-mile marathon?
Show answer
26.2 mi in km: 42.1648128
Frequently asked questions
What is the difference between area and perimeter?
Perimeter is the distance around; area is the space inside.
Why is area in square units?
Because you are counting unit squares that fill the shape.
Can two shapes have the same perimeter but different areas?
Yes. A 6 × 6 square and a 10 × 2 rectangle both have a perimeter of 24, but their areas are 36 and 20.
How do I find the area of an irregular shape?
Break it into simple shapes, find each area and add or subtract.
Try it yourself
Geometry CalculatorArea, perimeter, circumference, volume and surface area of common shapes.Circle CalculatorFind radius, diameter, circumference and area from any one of them.Unit ConverterConvert length, mass, temperature, volume, area and speed between metric and imperial units.Keep learning
Volume and Surface Area8 min readTypes of Triangles7 min readThe Pythagorean Theorem Explained6 min readWritten and reviewed by the SolveCalcPro editorial team. Spot a mistake? Tell us. See our editorial policy.