Answer :

As we know that,

From the above figure we see,

Diameter of bigger semi-circle, D = 42 cm

⇒ S1 and S4 are bigger semicircles with Radius, R = 21 cm

Also, S2, S3, S5 and S6 are smaller semi-circles with diameter, d equal to the radius of bigger semi-circle.

⇒ d = R

⇒ A_{B} = 693 sq.cm

Similarly,

⇒ A_{S} = 173.25 sq.cm

Area of shaded region = Area(S1) + Area(S4) + Area(S3) + Area(S6) – Area (S2) – Area(S5)

⇒ Area of shaded region = A_{B} + A_{B} + A_{S} + A_{S} – A_{S} - A_{S}

⇒ Area = 2 × A_{B}

⇒ 2 × 693 = 1386 sq.cm

∴ Area of shaded region is 1386 sq.cm

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