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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 \pi= 3.14).

In Figure, AB is a diameter of the circle, AC = 6 cm and BC = 8 cm. Find the area of the shaded region (Use p = 3.14).

Answers (1)

 [54.5 cm2]

Solution

Given: AC = 6cm and BC = 8cm

In the figure \triangle ABC is a right angle triangle.

Hence using Pythagoras theorem

\\(AB)^{2}=(AC)^{2}+(BC)^{2}\\ =(6)^{2}+(8)^{2}\\ =36+64\\ =100\\ AB=\sqrt{100}=10\\ AB=10 cm

Diameter of circle = AB = 10 cm

Radius =\frac{10}{2}=5 cm

Area of circle =\pi r^{2}

                 =3.14 \times (5)^{2}=78.5 cm^{2}

Area of \triangle ABC=\frac{1}{2}\times AC \times BC\\

                            =\frac{1}{2} \times 6 \times 8=24m^{2}

Area of shaded region = Area of circle – Area of DABC

                                               =78.5-24=54.5 cm2

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