Area and perimeter
Area is how big a surface is, and perimeter is how far it is all the way around. Choose the shape, enter the measurements, and see both the answer and how it is calculated.
The explanation is shown. Quick: rectangle, square, triangle and circle. Advanced: also triangle from three sides, parallelogram, trapezium and composite shapes — and the area in every unit.
Your numbers
Answer
How to work it out
- 1A = l · b = 6 · 4 = 24 cm²
- 2O = 2 · (l + b) = 2 · (6 + 4) = 20 cm
The formula
A = l · b
Length times width.
O = 2 · (l + b)
All four sides added together.
Area is always measured in square units: cm², m² … Perimeter is a length and is measured in cm, m …
In depth: more numbers and “what if”
The area in every unit
| Unit | Area |
|---|---|
| mm² | 2,400 |
| cm² | 24 |
| m² | 0.0024 |
| km² | 2.4 · 10^-9 |
What if every measurement is multiplied by k?
| k | Area | Circumference | Area multiplied by |
|---|---|---|---|
| 0.5 | 6 cm² | 10 cm | 0.25 |
| 0.9 | 19.44 cm² | 18 cm | 0.81 |
| 1 | 24 cm² | 20 cm | 1 |
| 1.1 | 29.04 cm² | 22 cm | 1.21 |
| 2 | 96 cm² | 40 cm | 4 |
The perimeter follows the measurements, but the area grows with k²: sides twice as long give four times the area.
More: Geometry
- PythagorasFind the missing side, set out a right angle, check whether a room is square, and find the space diagonal.
- Volume and surface areaBox, cylinder, cone, sphere, pyramid, prism, pipe and frustum — also in litres.
- The circleRadius, circumference and area from one measurement — plus sector, annulus, chord and rise.
- Right triangleSine, cosine and tangent: all sides and angles from two known values.
- AnglesThe third angle in a triangle and the angle sum of a polygon.
- Points in the coordinate systemDistance, midpoint and the line between two points — drawn in.
- Similar figuresScale factor and missing sides — area is multiplied by k², volume by k³.
- Any triangleThe sine and cosine rules: find the rest from SSS, SAS, ASA or SSA.
- TransformationsReflect, rotate and translate a figure on a coordinate grid — before and after.