Question

(b) In the figure (ii) given below, there are five squares each of side 2 cm.
(1) Find the radius of the circle.
(i) Find the area of the shaded region. (Take a = 3:14).

Answer 1

We have to find

(i) the radius of the circle

(ii) the area of the shaded region.

solution : see figure,

ON = OT + TN = 1 cm + 2 cm = 3 cm

AN = AB/2 = 2cm/2 = 1 cm

From ∆OAN,

OA² = ON² + AN²

⇒OA² = (3cm)² + (1cm)² = 10 cm²

⇒OA = √10 cm

Therefore the radius of the circle is √10 cm.

area of circle = πr² = π(√10 cm)² = 10 × 3.14 cm² = 31.4 cm²

Area of five squares = 5 × area of each square

= 5 × (side length)²

= 5 × (2 cm)²

= 5 × 4 cm²

= 20 cm²

Therefore the area of shaded region = area of circle - area of five squares

= 31.4 cm² - 20 cm²

= 11.4 cm²