Answer :

We know that, area of a square with side √a will be a.


[Area of square = (side)2]


Also, we can draw a square with area equal to a rectangle, we will use the area of rectangle in order to make the area equal to square.


side = √31 cm


Area of square = 31 cm2


Area of rectangle = length × breadth = 31 cm2


Here, let’s choose length = 6.2 cm and breadth = 5 cm


Construction steps:


1. Draw a rectangle ABCD with length, AB = 6.2 cm and breadth, BC = 5 cm.



2. Extend CD to CE, such that CE = BC = 5 cm.



3. Draw the perpendicular bisector of DE which bisects DE at O.



4. Taking O as center and OD = OE as radius, draw a semicircle.



5. Extend BC which intersects semicircle at F.



6. Draw a square CFGH taking CF as side.



Here,


Area of square CFGH = area of rectangle ABCD = 31 cm2.


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