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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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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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