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NCERT Class 6 Maths Chapter 10- Mensuration Revision Notes

Introduction to Mensuration

Mensuration

• Mensuration is the branch of mathematics that deals with the measurement of length, area or volume of various geometric shapes.

Shapes

• A shape is the form of an object.
• Examples of two-dimensional shapes are square, rectangle and triangle, and of three-dimensional shapes are cube, cuboid and sphere.

Perimeter

• Perimeter is the total length or total distance covered along the boundary of a closed shape.
• Perimeter of a circle is also called the circumference of the circle.

Perimeter of a Triangle

• Perimeter of triangle = Sum of lengths of all sides = a + b + c.
• If the given triangle is equilateral, that is if all the sides are equal (a = b = c), then its perimeter is equal to 3 × length of one side of the triangle.

Perimeter of a Rectangle

• Perimeter of a rectangle = 2 × (length + breadth)  

Perimeter of a Square

• Perimeter of square = 4 × length of a side = 4a

Perimeter of an ‘n’ sided polygon

• A polygon is a closed shape made up of line segments.
• Perimeter of n sided polygon = n× length of one side.
• Example: Length of each side of a hexagon is a cm, then:

Perimeter of the hexagon = 6a cm

Perimeter of Irregular Shapes

• Irregular shapes are the shapes which do not have all sides and angles equal.
• The perimeter of irregular shapes is equal to the total length covered by the shape.

Area

• Area is the total amount of surface enclosed by a closed figure.

Area of Square

• Area of a square = Side × Side =Side2=a2, where a is the length of each side.

Area of Rectangle

• Area = length ( l ) × breadth ( b)

Area of a Triangle

• Area of triangle = (1/2) × base × height = (1/2) × b × h

Areas of different types of triangles

• Consider an acute and an obtuse triangle.

Area of each triangle = (1/2) × base × height = (1/2) × b × h

Visualisation of Area

• Area of rectangle = l×b
• Area of square = a×a

Area of Irregular Shapes

• Area of an irregular figure can be calculated:

Step 1: Divide the irregular shape into regular shapes that you can recognize (e.g. triangles, rectangles, circles and squares)

• Step 2: Find the area of these individual shapes and add them. Sum will be the area of the irregular figure.

Example: Area of the given figure = Area of MNCB + Area of AMGH + Area of EFND

= [5 × 9 + 4 × 2 + 3 × 3] cm2

= [45 + 8 + 9] cm2

=62 cm2

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