1.

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)

Answer»

According to the question,

AC = 6 cm and BC = 8 cm

A triangle in a semi-circle with hypotenuse as diameter is right angled triangle.

Using Pythagoras theorem in right angled triangle ACB,

(AB)2 = (AC)2 + (CB)2

(AB)2 = (6)2 + (8)2

⇒(AB)2 = 36 + 64

⇒(AB)2 = 100 ⇒(AB)= 10

∴ Diameter of the circle = 10 cm

Thus, Radius of the circle = 5 cm

Area of circle = πr2

= π(5)2

= 25π cm2

= 25 × 3.14 cm2

= 78.5 cm2

We know that,

Area of the right angled triangle = ( ½ ) × Base × Height

= (½) × AC × CB

= (½) × 6 × 8

= 24 cm2

Now, Area of the shaded region = Area of the circle – Area of the triangle

= (78.5-24)cm2

= 54.5cm2



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