Question

a square OPQR is inscribed in a quadrant OAQB of a circle.
If the radius of circle is 6root2 cm, find the area of the shaded region.​

Answer 1

Step-by-step explanation:

radius is 6√2,

Then area of shaded region is 144/7m² or 20.57m² (approx.)

Answer 2

Area of shaded region = Area of quadrant - Area of square

• Radius of quadrant of circle - 6√2cm
• Area of quadrant = πr²/4
• Area = 18π cm²
• OQ forms the diagonal of square OPQR
• OQ = 6√2cm  (radius)
• In ΔOAQ, OA² + AQ² = OQ²
• 2OA² = 72  (OA =  AQ)
• OA² = 36
• OA = 6cm
• Area of square OPQR = side² = 36cm²
• Area of shaded region = 18π - 36 = 56.52 - 36
• Area = 20.52 cm².