Question

euen.
In Figure-8, a square OPQR is inscribed in a quadrant OA
If the radius of circle is 6/2 cm, find the area of the shaded region.
cribed in a quadrant OAQB of a circle.
Figure-8​

Answer 1

euen.

In Figure-8, a square OPQR is inscribed in a quadrant OA

Consider the attached figure while going through the following steps.

Given,

The radius of circle is 6/2 cm

A square OPQR is inscribed in a quadrant OAQB of circle

Area of shaded portion = Area of quadrant - Area of square

OQ = OA = OB = 6/2 cm

In Δ OQR,

OQ² = OR ² + QR²

as we have, (OP = PQ = QR = RO) sides of a square

⇒ OQ² = OR ² + OR² = 2OR²

(6/2)² = 2 OR²

OR = (6/2) √2

OR = 3/√2 cm

Therefore, the side of a square = a = 3/√2 cm

Area of quadrant OAQB = πr²/4

= 22/7 × (6/2)² × 1/4

= 7.07 cm²

Area of square OPQR = a²

= OR²

= (3/√2)²

= 9/2 = 4.5 cm²

Area of shaded portion = 7.07 - 4.5 = 2.57 cm²