Area using Perimeter

Area:
Area is a measure of  the outermost surface of an object. Area is a bounded space with its surrounding. Area is the  measure of  plane region or  amount at surface which any object occupies is called the area for that object. Area for any object is a measure ofbounded surface to its bounded space

Perimeter:
The length of the boundary of any closed figure is called its perimeter. The distance around a two-dimensional shape,for a circle perimeter is a circumference.closed surface for inner space occupied it said to be the perimeter for an object.

Finding Area using Perimeter For Square:

Area of Square =a2
Perimeter of Square =4a
Example 1:
For square board the perimeter is 84cm find the area for square board.

Solution:
we know perimeter is 84cm
for square perimeter,4a=84
a=84/4
a=21
area of square =a2
=212
area of square =441cm

Example 2:
The perimeter of a square playground is 1200m. Find its area using perimeter.

Solution :
Perimeter of the square ground, p = 4a
4a = p
a =p/4

Hence, a = 1200
4 m [since p = 1200 m ]
∴ a = 300 m
Area of the square ground A = a2
= 300 m × 300 m
Area = 90000 sq.m.

Finding Area using Perimeter For Rectangle:

Area of Rectangle =Length `xx` Breadth
Perimeter of rectangle =2(Length+Breadth)

Example 1:
If perimeter of rectangle is 18 m and its breadth 4m. find its area using perimeter.

Solution:
2 length + 2 breadth = perimeter
2l + 2`xx` 4 = 18
2l + 8 = 18
2l = 18– 8
2 l = 10
l =5
l=5,b=4
Now the area of the rectangle A = l `xx` b
= 5 m × 4 m
= 20 sq.m.

Example 2:
The perimeter of the floor of a rectangular room is 24 m and the  length is 7 m. Find its area.

Solution :
2 length + 2 breadth = perimeter
2 × 7 + 2b = 24
14 + 2b = 24
2b = 24 – 14
2 b = 10
b =`10/2`
= 5
Now the area using perimeter of  rectangle A = l` xx` b
= 7 m × 5 m
= 35 sq.m.