Question

A square OABC is inscribed in a quadrant OPBQ a circle.if OA= 21 cm,find the area of the shaded region.

Answer 1

Solution:-
In Δ OAB,
OB² = OA² + AB²
OB² = 21² + 21²
OB² = 441 + 441
OB² = 882
OB = √882
OB = 29.698 cm
Now, OB = 29.698 cm is the radius of the circle.
Area of quadrant = 90°/360° × 22/7 × (29.698)²
= 1/4 × 22/7 × 882
= 19404/28
Area of the quadrant = 693 sq cm
Now, area of the square OABC = 21 × 21
= 441 sq cm
Area of the shaded region = area of quadrant - area of square 
= 693 - 441
Area of the shaded region = 252 sq cm.
Answer.

Answer 2

Side of square = 21 cm

their diagonal of square = 21 x root 2 = radius of quadrant

area [shaded region] = ar [quadrant] - ar [square]

= 1/4 x π × r∧2  - side∧2

= 1/4 × 22/7 × [21 root2]∧2 - 21∧2

= 1/2 × 11/7 × 21 × 21 × 2  - 441

= 693  - 441

= 252cm∧ 2