Page 179 - Start Up Mathematics_4

Perimeter
Mr Verma wants to fence his garden to protect it
from animals.

To find out how much wire he needs, he takes a long
rope and ties a knot at its end. Then he starts moving
from one corner of the garden along its boundary
to the next corner. He ties a knot in the rope at this
point. Then he moves further and at every corner
he ties a knot.

When he reaches the corner from where he had started, he ties the last knot. The rope looks
like this:

He now measures the rope from the first knot to the last knot and finds it to be 20 m long.
This length around the garden is its perimeter.
Perimeter is the total length of the boundary of a plane closed figure. The word perimeter
is derived from the Greek word “Peri” meaning “around” and “meter” meaning “measure”. In
short, perimeter means the total of all sides of a given plane figure.
2 cm
Example 3: Find the perimeter of the given figure.
4 cm 4 cm
Solution: Perimeter = 2 cm + 4 cm + 6 cm + 4 cm = 16 cm

Perimeter of a rectangle 6 cm
In rectangle ABCD, AB = DC and AD = BC.
D 5 cm C
Perimeter of ABCD = AB + BC + CD + DA

= 5 cm + 3 cm + 5 cm + 3 cm 3 cm 3 cm
= (2 × 5) cm + (2 × 3) cm
A B
= 10 cm + 6 cm = 16 cm 5 cm

Thus, we can say that the perimeter of a rectangle = (2 × Length) + (2 × Breadth)
= 2 × (Length + Breadth)

Perimeter of a square

In square PQRS, PQ = QR = RS = SP S 3 cm R

Perimeter of PQRS = PQ + QR + RS + SP
3 cm 3 cm
= 3 cm + 3 cm + 3 cm + 3 cm
= 4 × 3 cm = 12 cm P Q

Thus, we can say that the perimeter of a square = 4 × Side 3 cm

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