Definitions [2]
Polygon: Polygon refers to a closed 2D shape which is made up of a finite number of line segments, but the perimeter is a one-dimensional measurement.
Area of a circle: The area of a circle is the region occupied by the circle in a two-dimensional plane.
Formulae [13]
Perimeter = Sum of all side lengths

Perimeter of a rectangle = 2 × length + 2 × breadth
P = 2(1 + b) ⇒ (i) l = `P/2` − b, i.e., length = `"Perimeter"/2` − breadth
(ii) l = `P/2` − l, i.e., breadth = `"Perimeter"/2` − length
Perimeter of Square = Total boundary of the square
= Side + Side + Side + Side
P = 4 × Side
Or: P = 4s (where 's' represents the side length)
side = ` "perimeter"/"4"`
Always include the correct linear unit (cm, m, mm, km, etc.)
Perimeter of a Triangle = 3 × length of a side.
The perimeter of a regular polygon = (length of one side) × number of sides.
The perimeter of an Irregular polygon = Sum of all sides of Irregular polygons.
Area = Amount of space inside a flat shape
Area of square = side × side
= s × s
= s2
Area of square = (side)²
⇒ its side = \[\sqrt{Area}\]
Area of a rectangle = length × breadth
Written as: A = l × b
l = `A/b` i.e., length = `"Area"/"Breadth"`
and, b = `A/l` i.e., breadth = `"Area"/"Length"`
The area of each congruent part = `1/2` (The area of the rectangle)
Area of parallelogram = base x height
Area of triangle = `(1/2) × "base" × "height" = 1/2 × b × h`.
Area of the circle = πr2
| Shape | Formula |
|---|---|
| Rectangle | P = 2 × (l + b) |
| Square | P = 4 × side |
| Equilateral Triangle | P = 3 × side |
| Regular Pentagon | P = 5 × side |
| Regular Hexagon | P = 6 × side |
Concepts [18]
- Basic Concepts in Mensuration
- Concept of Perimeter
- Perimeter of a Rectangle
- Perimeter of Squares
- Perimeter of Triangle
- Perimeter of Polygon
- Concept of Area
- Area of Square
- Area of Rectangle
- Triangles as Parts of Rectangles and Square
- Generalising for Other Congruent Parts of Rectangles
- Area of a Parallelogram
- Area of a Triangle
- Circumference of a Circle
- Area of Circle
- Conversion of Units
- Problems based on Perimeter
- Problems based on Area

