Question

If the following figure OAQB is a
Quadratic of a circle, OPQR is
a square. If op=10cm.
Find the area of the shaded
region.​

Answer 1

The area of the shaded  region is:​

Please see the attachment for the complete question and solution.

Answer 2

In the following figure OAQB is a  Quadratic of a circle, OPQR is  a square. op=10cm.

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

                                      = πr²/4 - s²

                                      = π(OQ)²/4 - OP²

OP = 10 cm

⇒ OP = OR = OR = QR = 10 cm (sides of a square)

In Δ OQR,

OQ² = OR² + QR²

= 10² + 10²

OQ² = 200

OQ = 10√2 cm

The radius of the quadrant = OA = OQ = OB = 10√2 cm

Area of shaded region = π (10√2)²/4 - 10²

= π (200)/4 - 100

= 22/7 × 200/4 - 100

= 157.14 - 100

= 57.14 cm²