Question

A rectangle and a square have equal perimeters. The length and breadth of the rectangle are 26 cm and 10 cm respectively .find the area of the square.

Answer 1

Hint: We know that perimeter is defined as the sum of all sides. For all types of figure we have different formulas respectively .Here we will use formulas of perimeter for both figures to find out side of square and using formula for area of square we will get area of square. Firstly we will find perimeter of rectangle then we will perimeter of square then using perimeter we will find out side of square and then we get area of square.

Formula used: Perimeter of rectangle \[ = 2\left( {l + b} \right)\]
Perimeter of square \[ = 4 \times {\text{side}}\]
Area of square \[ = {\text{side}} \times {\text{side}}\]

Complete step-by-step answer:
We have
Length of rectangle = \[26cm\]
Breadth of rectangle = $10cm$
Perimeter of rectangle \[ = 2\left( {l + b} \right)\]
Putting value of length and breadth of rectangle in formula
  \[ = 2\left( {26 + 10} \right)cm = 2\left( {36} \right)cm = {{7}}2cm\]
According to question,
We have ,
Perimeter of rectangle = Perimeter of square
Therefore we get,
Perimeter of square \[ = 72{{ }}cm\]
Now we will use formula of Perimeter of square to find out side of square
Perimeter of square \[ = 4 \times {\text{side}}\]
$\Rightarrow$\[72{{ }}cm = 4 \times {\text{side}}\]
$\Rightarrow$$\dfrac{{72cm}}{4} = side$
$\Rightarrow$$18cm = side$
Now we will find area of square,
\[{\text{Area of square}} = {\text{side}} \times {\text{side}}\]
Putting $18cm = side$
\[{\text{Area of square}}= 18cm \times 18cm = 324{{ }}c{m^2}\]

Therefore the area of the square is \[324{{ }}c{m^2}\]

Note: A square is a quadrilateral in which all sides are equal and a rectangle is quadrilateral in which opposite sides are equal. Similarity between both of them is they both have right angles $(90^\circ)$ at their corners and diagonals are also equal.
Square and rectangle both are considered as special types of quadrilateral with $90^\circ$.