In the given figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.

in fig abc is a quadrant of a circle of radius 14 cm and a semi circle is  drawn with bc as diameter find the area of shaded region - Mathematics -

Asked by Pragya Singh | 1 year ago |  163

1 Answer

Solution :-

Radius of the quadrant ABC of circle = 14 cm

AB = AC = 14 cm

BC is diameter of semicircle.

ABC is right angled triangle.

By Pythagoras theorem in ΔABC,

BC= AB+AC2

⇒ BC= 14+142

⇒ BC = \( 14\sqrt{2}\) cm

Radius of semicircle = \( \dfrac{14\sqrt{2}}{2} \) cm = 7\( \sqrt{2}\) cm

Area of ΔABC = (\( \dfrac{1}{2}\))×14×14 = 98 cm2

Area of quadrant = \( (\dfrac{1}{4})×(\dfrac{22}{7})×(14×14)\) = 154 cm2

Area of the semicircle = \( (\dfrac{1}{2})×(\dfrac{22}{7})×7\sqrt{2}×7\sqrt{2}\) = 154 cm2

Area of the shaded region =Area of the semicircle + Area of ΔABC – Area of quadrant

= 154 +98-154 cm= 98cm2

Answered by Abhisek | 1 year ago

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