Question 63

The perimeter of a square and a circle are same. If the area of the circle is 1386 $$cm^2$$, then what will be the area of the square?

Solution

Given, Area of the circle = $$1386 cm^2$$
Let the radius of the circle be r cm.
$$\dfrac{22}{7} \times r^2 = 1386$$

=> $$r^2 = 441$$
=> $$r = 21$$
Radius of the circle = 21 cm
Circumference of the circle = $$2\times\dfrac{22}{7} \times21 = 132 cm$$
Circumference of circle = Perimeter of square = 132 cm
Let side of the square be a cm.
4a = 132 =>a = 33 cm
Therefore, Area of the square = $$a^2 = 33^2 = 1089 cm^2$$


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