Draw a square of

Steps of construction:

1. Draw a line BC = 5 cm, taking B and C as centres, draw

∠ABC = ∠BCD = 90°, such that AB = CD = 3 cm

2. Join AD to get rectangle ABCD, here area(ABCD) = length × breadth = 5 × 3 = 15 cm.

3. From the rectangle drawn, extend AD by 3 cm to D'.

4. From the mid–point of AD'(Let it be O such that OA = OD'=4 cm) Draw a circle taking OA = OD' as radius.

3. Now, draw a chord PQ ⊥ AD', passing through D.

6. Taking DP as side, draw a square DPRS, which is required.

Concept used:

The area of rectangle form of parts into which a diameter of a circle is cut by a perpendicular chord is equal to the area made by the square of half the chord.

And in the diagram, we made, AD' is diameter and PQ is perpendicular chord, therefore

Area(DPRS) = ar(ABCD) = 15 cm²

And DPRS is a square