Q) In Figure, a square OABC is inscribed in a quadrant OPBQ. If OA = 15 cm, find the area of the shaded region. (Use π = 3.14).

Ans: 

Step 1: In the figure, we have a quadrant OPBQ (quarter part of circle, with center O). Inside this quadrant, a square OABC is inscribed and side of square is 15 cm.

Approach: The shaded region area can be calculated by subtrating square area from quadrant area. 

Step 2: Radius of the quadrant in the given figure = diagonal of the square.

∵ Diagonal of square = √2 × side

= √2 × 15 = 15√2 cm

∴ Radius of the Quadrant, r = 15√2 cm

Step 3: ∵ Area of the quadrant = () π r ² 

= × 3.14 × (15√2) ²

= × 3.14 × 225

= 353.25 cm²

Step 4: ∵ Area of the square  = side ²

= 15 ² =  225 cm²
Step 5:  Area of shaded regions = Area of quadrant – Area of square

= 353.25 – 225 = 128.25 cm²

Therefore, the area of shaded region is 128.25 cm²

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