Area and Perimeter Calculator
How to Calculate Area and Perimeter
Understanding the difference between area and perimeter is fundamental to geometry. While they both measure a shape, they describe two very different properties.
1. Rectangles and Squares
A rectangle is a four-sided shape where opposite sides are equal. A square is a special type of rectangle where all four sides are equal.
- Rectangle Perimeter: P = 2 × (Length + Width)
- Rectangle Area: A = Length × Width
- Square Perimeter: P = 4 × Side
- Square Area: A = Side²
2. Circles
In a circle, the perimeter is often called the circumference. You need the radius (distance from center to edge) to calculate both metrics.
- Circumference: C = 2 × π × r
- Area: A = π × r²
- Note: We use 3.14159 as the value for Pi (π).
3. Triangles
The perimeter is simply the sum of all sides. For the area, this calculator uses Heron's formula, which allows calculation based on side lengths alone.
- Perimeter: P = Side A + Side B + Side C
- Area: Using semi-perimeter s = (A+B+C)/2, then Area = √[s(s-a)(s-b)(s-c)]
Realistic Examples
Fencing a Yard: If you have a rectangular yard that is 50 meters long and 30 meters wide, the perimeter tells you how much fencing you need (50+30+50+30 = 160m). The area tells you how much grass seed you need (50 × 30 = 1,500m²).
Circular Table: A circular dining table with a radius of 1 meter has a surface area of approximately 3.14 square meters and needs about 6.28 meters of decorative trim around the edge.