Page 133 - Maths Skills - 7

Perimeter and Area 131

INTRODUCTION
Sabir and Rekha made pictures. Sabir made his picture on a rectangular sheet of length 60 cm and breadth 20 cm
while Rekha made hers on a rectangular sheet of length 40 cm and breadth 35 cm. Both these pictures have to be
separately framed and laminated. Who will have to pay more for framing, if the cost of framing is ` 3.00 per cm?

If the cost of lamination is ` 2.00 per cm , who has to pay more for lamination?
2
For finding the cost of framing, we need to find perimeter and then multiply it by the rate for framing. For finding
the cost of lamination, we need to find area and then multiply it by the rate for lamination.

PERIMETER
The sum of the measures of all the sides of a closed plane figure is called the perimeter. As it is the length of all
the sides sum up together so its unit is same as the unit of length, i.e., m, cm, mm, km, etc.

Perimeter of a Square D Side C
P
P = 4 × side Side of a square = 4
Side Side
where P stands for perimeter.

Perimeter of a Rectangle A Side B
If P is the perimeter of rectangle of length ‘l’ and breadth ‘b’ then

P = 2 (l + b) l

P P b
‘l’ of rectangle = – b ‘b’ of rectangle = – l
2 2
With the help of the above two formulae, you may also find the length or breadth of a rectangle if perimeter and
breadth or length are given respectively.
A
Perimeter of a Triangle
If ‘a’, ‘b’ and ‘c’ are the three sides of a scalene triangle, then perimeter (P) of the triangle ABC c b
is given by
P = a + b + c B a C

Perimeter of an Isosceles Triangle
Let XYZ be an isosceles triangle with XY = XZ. Then the perimeter (P) of the triangle XYZ is given by

P = XY + YZ + XZ
= 2XY + YZ [Q XY = XZ]
or, P = 2XZ + YZ

Perimeter of an Equilateral Triangle
In an equilateral triangle, the length of all the sides is equal. Let DABC be an equilateral triangle with each side
of length ‘a’, then perimeter (P) of DABC is given by:

P = AB + BC + CA
= a + a + a = 3a = 3 × side [Q AB = BC = CA = a]