Lesson BASIC FORMULAE FOR FINDING AREA AND PERIMETER OF A RECTANGLE.

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The basic formulae for Finding the area and perimeter of a rectangle is designed to help you know the appropriate formula to use when dealing with area and perimeter of a rectangle.
 
          AREA OF A RECTANGLE 
 
   An area (A) of a rectangle is a space covered by that rectangle.The area is given by;

A=L*W

where 
A=area,L=length of the rectangle,W=width of the rectangle.

EXAMPLE 1:
Find the area of a rectangle given that its length of width is 4cm and 2cm respectively.

Solution.
A=L*W
but L=4cm,W=2cm
Therefore,
A=4cm*2cm
A=8cm^2
The area of the rectangle is 8cm*2

EXAMPLE 2:
Find the length of a rectangle given that its area is 8cm^2 and its width is 2cm.

SOLUTION      
A=L*W
from the question,A=8cm^2 and W=2cm
Then,
8=L*2
8=2L
divide both side by 2
8/2 = 2L/2
4=L
i.e, L=4cm.
The length of the rectangle is 4cm.

PERIMETER OF A RECTANGLE.
 
  Perimeter (P) of a rectangle is the sum of the four sides of the rectangle.
Note:rectangle has four sides of which two opposite sides are equal.(i.e two length equal and two width equal.)
 Now if we add these sides,we have that  
perimeter (P)=L+L+W+W
     P=2L+2W
P=2(L+W)------This is the formula for perimeter of a rectangle.

EXAMPLE 3:
A rectangle has a length of 4cm and width of 2cm.find its perimeter.
        
        SOLUTION 
Using perimeter formula,
P=2(L+w)
But L=4cm,w=2cm      
   Then,
P=2(4cm+2cm)
P=2(6cm)
P=12cm.
The perimeter of the rectangle is 12cm.
 
Note:The unit of area is squared unit but that of perimeter is not.

AREA AND PERIMETER RELATIONSHIP. 
 
    Sometimes,you may be given area and perimeter of a rectangle which you may be required to find its length and width.To tackle this type of problem,study example 4 below.

EXAMPLE 4:
The area of a rectangle is 6cm^2 and its perimeter is 10cm.find the length and width of the rectangle.
 
       SOLUTION
From the above,
Area (A) is 6cm^2
i.e. 
LW=6------(1)
also,
perimeter (P)=10cm
ie
2(L+W)=10-----(2)
divide both side of equation 2 by 2
L+W=5------(3)
from equation 3,,
L=5-W------(4)
put (4) in (1)
(5-W)W=6  
 5W-W^2-6=0
W^2-5W+6=0
factories the quadratic equation
(W-2)(W-3)=0
Therefore,
W=2cm or W=3cm
When W=2cm
from (4) 
 L=5-2
L=3cm
Hence,the length and width of the rectangle is 3cm and 2cm respectively.