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प्रश्न
In figure, AB is a diameter of the circle, AC = 6 cm and BC = 8 cm. Find the area of the shaded region (Use π = 3.14).
उत्तर
Given, AC = 6 cm and BC = 8 cm
We know that, triangle in a semi-circle with hypotenuse as diameter is right angled triangle.
∴ ∠C = 90°
In right angled ΔACB, use Pythagoras theorem,
∴ AB2 = AC2 + CB2
⇒ AB2 = 62 + 82
⇒ AB2 = 36 + 64
⇒ AB2 = 100
⇒ AB = 10 cm ...[Since, side cannot be negative]
∴ Area of ΔABC = `1/2 xx "BC" xx "AC"`
= `1/2 xx 8 xx 6`
= 24 cm2
Here, diameter of circle,
AB = 10 cm
∴ Radius of circle,
r = `10/2` = 5 cm
Area of circle = πr2
= 3.14 × (5)2
= 3.14 × 25
= 78.5 cm2
∴ Area of the shaded region = Area of circle – Area of ΔABC
= 78.5 – 24
= 54.5 cm2
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