Mensuration:Mensuration is a branch of mathematics which is a topic in Geometry. It is a study of various geometrical shapes, their length, breadth, volume, and area for 2D as well as 3D shapes. Some important terminologies included in this topic are covered below.
Closed figure:A figure with no open ends is a closed figure.
Regular closed figures: A closed figure in which all the sides and angles equal.
Perimeter is the distance covered along the boundary forming a closed figure when we go round the figure once. The concept of perimeter is widely used in real life.
Eg: 1) For fencing land.
2) For building a compound wall around a house.
The perimeter of a regular closed figure is equal to the sum of its sides.
Perimeter of a rectangle:
= Length(l) + Breadth(b) +Length(l) + Breadth (b)
= 2 (l + b)
Perimeter of a square:
A triangle with all its sides and angles equal is called an equilateral triangle.
The perimeter of an equilateral triangle with the side 'a'=a+a+a =3 x a
The amount of surface enclosed by a closed figure is called its area. The following conventions are to be adopted while calculating the area of a closed figure using a squared or graph paper.
1. Count the fully-filled squares covered by the closed figure as one square unit or unit square each.
2. Count the half-filled squares as half a square unit.
3. Count the squares that are more than half-filled as one square unit.
4. Ignore the squares filled less than half.
For example, the area of this shape can be calculated as shown:
Area estimate (sq. units)
Fully filled squares
7 x 1/2
Squares filled more than half
Squares filled less than half
Area covered by full squares = 6 x 1 = 6 sq. units Area covered by half squares = 7 x ½ = 7/2= 3 ½ sq. units.
Total area of the given shape = 6 + 3 ½ sq. units Thus, the total area of the given shape = 9 ½ sq. Units.
Area of a rectangle can be obtained by multiplying length by breadth. Area of the square can be obtained by multiplying side by side.