Mensuration

Definition:

Mensuration is branch of mathematics which is concerned about the measurement of length, area and Volume of plane and Solid figure

Perimeter & Area of Common & Known Shapes

Perimeter

• The perimeter of plane figure is defined as the length of the boundary outline of the figure
• It units is same as that of length i.e. m, cm, km etc 

Area

• The area of the plane figure is the surface enclosed by its boundary
• It unit is square of length unit. i.e. m² ,  km² etc

Area and Perimeter of Plane figures 

Rectangle

Perimeter of Rectangle, P

= 2(Length + Breadth)    

or   2(Length + Width)

⇒P = 2(L+B)  or  2(L+W)

Area of Rectangle (A)

=Length × Breadth        

or    Length × Width

A = L× B     or    L × W

L, B and W are Length, Breadth or Width of the rectangle

Example 1

Find the total distance around the rectangular field, if the length of the field is 35 meters and width is 28 meters. Also find the area of the field.

Solution:

Length of the field = 35 meters

Width of the field = 28 meters

Using the formula of perimeter of a rectangle

Perimeter 

= 2 (Length + Width)

= 2 (35 + 28) meters

= 2 x 63 meters 

= 126 meters

 Area of rectangular field  =Length x width 

= 35 × 28

= 980 metre²

 Example 2

A rectangular ground is 8 m long and 5 m wide such that there is a margin of 1.5 m along each of its sides. Find the total area of the margin.

Solution: 

Length of the rectangular ground

= 8 m

Breadth of the rectangular ground

= 5 m

Then,

Area of the rectangular ground

= length × breadth 

= 8 × 5

= 40 m²

By removing the 1.5m margins, new length and breadth of the ground are:

New Length

= 8 – (1.5 + 1.5) = 5 m

New Breadth

= 5 – (1.5 + 1.5) = 2 m

New area of the ground

= 5m × 2m = 10 m²

Therefore,

Area of margin

= Area of the rectangular

ground with margins –

Area of the ground

without margins 

= 40 – 10

= 30 cm²

Hence, the required area

is 30 cm²

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Himura Kenshin

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