Area and perimeter are important measurements used to describe polygons, which are closed two-dimensional shapes with straight sides.
The formulas for calculating the area and perimeter of various polygons depend on the specific type of polygon.
Let’s explore the formulas for some common polygons:
- Rectangle:
- Area: A = length × width
- Perimeter: P = 2 × (length + width)
- Square:
- Area: A = side × side (or A = side^2)
- Perimeter: P = 4 × side
- Triangle: There are different formulas for the area of a triangle based on the information given:
- If the base (b) and height (h) are known: Area: A = (1/2) × base × height
- If the lengths of all three sides (a, b, c) are known (Heron’s formula): Semi-perimeter: s = (a + b + c) / 2 Area: A = √(s × (s – a) × (s – b) × (s – c))
- If the triangle is a right-angled triangle, with one angle measuring 90 degrees: Area: A = (1/2) × base × height (where base and height are the two sides that form the right angle)
- Regular Polygon: For a regular polygon with n sides and side length s:
- Area: A = (1/4) × n × s^2 × cot(π/n)
- Perimeter: P = n × s
- Circle:
- Area: A = π × radius^2
- Perimeter (Circumference): C = 2 × π × radius
- Parallelogram:
- Area: A = base × height
- Perimeter: P = 2 × (side1 + side2)
- Trapezoid:
- Area: A = (1/2) × (sum of parallel sides) × height
- Perimeter: P = sum of all sides