Area and perimeter are two basic quantities that describe geometric figures. The area tells us how much surface a figure takes up, while the perimeter tells us how long its edge is. Knowing the formulas lets you calculate how much paint to buy for a wall or how much fencing for a fence. In this article we gather the most important formulas and show examples.
Area versus perimeter — what's the difference?
It is worth distinguishing between these two concepts:
- Perimeter is the sum of the lengths of all the sides of a figure, expressed in units of length (m, cm).
- Area is a measure of the surface inside a figure, expressed in square units (m², cm²).
Formulas for basic figures
The most commonly used formulas for area and perimeter:
- Square: perimeter L = 4 × a, area P = a²
- Rectangle: perimeter L = 2 × (a + b), area P = a × b
- Triangle: perimeter L = a + b + c, area P = ½ × a × h (base times height divided by two)
- Circle: perimeter (circumference) L = 2 × π × r, area P = π × r²
The symbol a stands for the length of a side, b for the second side, h for the height, r for the radius, and π is the number pi, approximately 3.14.
Example: rectangle
A plot of land has the shape of a rectangle with sides a = 8 m and b = 5 m. We calculate the area and the perimeter.
- Area: P = a × b = 8 × 5 = 40 m².
- Perimeter: L = 2 × (a + b) = 2 × (8 + 5) = 2 × 13 = 26 m.
The plot has an area of 40 m², and 26 metres of fencing are needed for the fence.
Example: circle
A round pool has a radius of r = 3 m. We calculate the area and the circumference.
- Area: P = π × r² = 3.14 × 3² = 3.14 × 9 = 28.26 m².
- Circumference: L = 2 × π × r = 2 × 3.14 × 3 = 18.84 m.
The surface of the water is about 28.26 m², and the edge of the pool is about 18.84 m long.
Units and conversions
With areas it is easy to make a mistake in the units:
- 1 m² = 10 000 cm²
- 1 are = 100 m²
- 1 hectare = 10 000 m²
All the sides of a figure must be expressed in the same unit before you substitute them into the formula.
Example: triangle
A triangle has a base of a = 10 cm and a height of h = 6 cm. We calculate the area.
- We apply the formula P = ½ × a × h.
- We substitute: P = 0.5 × 10 × 6.
- We calculate: P = 30 cm².
The area of the triangle is 30 cm². Remember that the height must be perpendicular to the base it refers to.
Practical applications
Formulas for area and perimeter come in handy in many everyday situations:
- Area — calculating the amount of paint for a wall, panels for a floor or tiles for a terrace.
- Perimeter — working out the length of skirting board, fencing for a fence or tape for an edging.
Always add a few per cent of spare material for offcuts and possible mistakes.
Most common mistakes
- Confusing area with perimeter — we calculate area in square units, perimeter in units of length.
- Omitting the factor of ½ in a triangle — the area of a triangle is half the product of the base and the height.
- Using the diameter instead of the radius — the circle formulas use the radius r, that is half the diameter.
- Inconsistent units of the sides — all the dimensions must be in the same unit.
Frequently asked questions
- What is the number pi? It is a constant equal to about 3.14, describing the ratio of the circumference of a circle to its diameter.
- How do I calculate the area of an irregular plot? You divide it into simpler figures (rectangles, triangles), calculate their areas and add up the results.
- What is the diameter? A segment passing through the centre of a circle, equal to twice the radius.
Summary
The perimeter is the length of the edge of a figure, while the area is a measure of its surface. Each figure has its own formulas: for the square, rectangle, triangle and circle. Keep an eye on the units and remember that area is expressed in square units.
Calculate the area and perimeter of figures: Figure Area Calculator →