Questions: Area of Rectangle

In this post we will discussed questions related to area of rectangle and area of square. All the questions are fully solved for your understanding so that you grasp the concept and solve the question on your own without any help.

Some notable formulas which you should remember for this topic are:
Area of Square = Side * Side
Area of Rectangle = Length * Breadth
Perimeter of Rectangle = 2 * (Length + Breadth)

Equipped with the above formula you can solve majority of questions of this topic. In case if you have any doubt, feel free to ask in comment section.

Area of Rectangle Questions

In Rectangle ABCD,
Let Breadth = B cm
and Length of rectangle = B + (20/100)*B => B+ 1/5 B => 6B/5 cm

Area of Rectangle = L * B

According to question,
Sides of the square PQRS = B cm

We know that area of square = Side * Side
==> B * B
==> { B }^{ 2 }

Now according to question, the ratio between area of rectangle and square

\frac { Area\quad of\quad Rectangle\quad ABCD }{ Area\quad of\quad square\quad PQRS } =\frac { \frac { 6{ B }^{ 2 } }{ 5 }  }{ { B }^{ 2 } }\\\ \\\frac { Area\quad of\quad rectangle\quad ABCD }{ Area\quad of\quad Square\quad PQRS } =\quad \frac { 6 }{ 5 } 

Hence 6 : 5 is the required ratio

Area of rectangle = 460 meters
Area of Rectangle = Length * Breadth

Let Breadth = B Meters

And Length = B + 15% of B
Length => B + (15/100) * B => 23B/20

Now
Area = Length * Breadth

460\quad =\frac { 23B }{ 20 } \times \quad B\\\ \\ { B }^{ 2 }=\frac { 460\quad \times \quad 20 }{ 23 } \\\ \\ { B }^{ 2 }\quad =\quad 400\\\ \\ B\quad \quad =\quad 20\quad \\ 

Hence the breadth of the rectangle is 20 meters

Now the cost of fencing per meter is Rs 26.50
Then
=> 26.50 * ( 4B + 40) = 5300
=> 106B + 1060 = 5300
=> 106B = 5300-1060
=> 106B = 4240
=> B = 4240/106
=> B = 40 meter

We know that,
Length = B + 20 => 40 + 20 => 60 meters

Hence the length of the plat is 60 meters

Now, after increasing 30% length we will get new rectangle of larger size

Length\quad =\quad L\quad +\quad \frac { 30 }{ 100 } \times \quad L\\\ \\ Length\quad =\quad \frac { 13 }{ 10 } \quad L

The breadth of the rectangle will remain the same
Breadth = B

So, the new area of rectangular plot = New length * Breadth

New\quad Area\quad of\quad Rectangular\quad Plot\quad =\quad \frac { 13L }{ 10 } \times \quad B\\\ \\ New\quad Area\quad of\quad Rectangular\quad Plot\quad =\quad \frac { 13 }{ 10 } \times \quad Original\quad Area\\ \\ 

Hence the ratio of new area to old area is ==> 13 : 10

From the above information,
Area of Road = Area of Outer Rectangle – Area of Inner Rectangle

Area of Road = 1764 sq. meters

Let us assume that the side of bigger plot ABCD = a meters
So the area of bigger plot will be =\quad { a }^{ 2 } equation –(2)

Now the side of inner plot be = (a – 6) meters
The area of inner plot will be = \quad { (a-6) }^{ 2 }\ \ \ equation—–(3)

\quad { 1764\quad ={ a }^{ 2 }\ -\ (a-6) }^{ 2 }\\\ \\ 1764=\ { a }^{ 2 }-\ { a }^{ 2 }+36-12a\\\ \\ 12a=1728\\\ \\ a=144\quad meters\\ \\ 

Perimeter of the outer edge of the road = 4 * sides
==> 4 * 144
==> 576 meters

Let the length of rectangular plat = L
And Breadth of Rectangular Plot = B

Area of Rectangular Plot = L * B

Now,
Length is increased by 50% => L + 1/2 L => 3L/2
Breadth is increased by 20% => B + 1/5 B => 6B/5 {20% = 1/5}

The new area is ==> (3L/2) * (6B/5) ==> 9LB/5 {original area = L*B}
This means that the new area is 9/5 times the original area

Let the breadth of rectangle = B cm
Then length of rectangle = B + (60/100)B => 160/100 B => 8B/5

Difference between length and breadth = 24 cm
So,
==> L – B = 24 cm
==> (8B/5) – B = 24 cm
==> \frac { 8B-5B }{ 5 } =\ 24\quad cm\ \
==> 3 B = 24 * 5
==> B = 40 cms

And similarly L = 64 cms

Area of Rectangle = L * B => 64 * 40 => 2560 sq. cm
Hence the area of rectangle is 2560 sq cm

Let the side of square ABCD = L cm
Area of square = L * L = { L }^{ 2 }

Let the breadth of rectangle = L cm
Length of rectangle = (L+ 5) cm

\frac { Length\quad of\quad rectangle }{ Breadth\quad of\quad rectangle } =\frac { 3 }{ 2 } \\\ \\ \\ \frac { L\quad +\quad 5 }{ L } =\frac { 3 }{ 2 } \\ 

2L + 10 = 3L
L = 10 cm

Therefore, original area of square = 10 * 10 =>100 sq cm