Question

# Question 7 In figure , BC is a diameter of the circle, AC = 6cm and AB = 8 cm. Find the area of the shaded region. (use π=3.14)

Solution

## Given: AC = 6 cm and AB = 8cm We know that, triangle in a semi – circle with hypotenuse as diameter is right angled triangle. ∴∠A=90∘ In right angled ΔACB, use Pythagoras Theorem ∴BC2=AC2+BA2 ⇒BC2=62+82=36+64 ⇒BC2=100 ⇒BC=10 cm  [ Since length of a side cannot be negative] ∴ Area of ΔABC=12×AB×AC=12×8×6=24 cm2 Here, diameter of circle, AB = 10 cm Radius of circle r=102=5 cm Area of circle =pir2=3.14×(5)2 =3.14×25=78.5 cm2 Area of the shaded region = Area of circle - Area of ΔABC 78.5−24=54 cm2

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