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Sum

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).

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#### Solution

Identify the figure as a circle, and a right-angled triangle (and semicircle, segment also), because AOB is diameter and angle in semicircle, is 90°.

So, ∠C = 90°

In right angled ΔABC,

b = base = BC = 8 cm

a = altitude = AC = 6 cm

By Pythagoras theorem in right ΔABC,

AB^{2} = BC^{2} + AC^{2}

= 8^{2} + 6^{2} = 64 + 36

⇒ AB^{2} = 100 cm

⇒ AB = 10 cm

Hence, r = `10/2` = 5 cm

∴ Area of shaded region = Area of circle – Area of right ΔABC

= `pir^2 - 1/2` Base × Alt.

= `3.14 xx 5 xx 5 - 1/2 xx 8 xx 6`

= `3.14 xx 25 - 8 xx 3`

= (78.50 – 24) cm^{2}

= 54.50 cm^{2}

∴ Area of shaded region = 54.50 cm^{2}

Concept: Areas of Combinations of Plane Figures

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