Question

In the given figure, a square OABC has been inscribed in the quadrant OPBQ. If OA = 20 cm, then the area of the shaded region is ______.

Options

• 214 cm²

• 228 cm²

• 242 cm²

• 248 cm²

Answer 1

In the given figure, a square OABC has been inscribed in the quadrant OPBQ. If OA = 20 cm, then the area of the shaded region is 228 cm².

Explanation:

Join OB.

Now, OB is the radius of the circle.

We have : 

OB² = OA + AB [By pythagoras' therom]

⇒ OB² = {(20)² + (20)²} cm2

⇒ OB² = (400 + 400) cm²

⇒ OB² = 800 cm²

`=> "OB" =20sqrt2  "cm"`

Hence, the radius of the circle is `20sqrt(2)  "cm".`

Now,

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

`=|(1/4xx3.14xx20sqrt(2)xx20sqrt(2))-(20xx20)| "cm"^2`

`=|(1/4xx314/100xx800)-400| "cm"^2`

= (628 - 400) cm² 

= 228 cm²