Question

find the area of the shaded region where a circular arc of
radius 7 cm has been drawn with vertex of an equilateral triangle OAB
of side 14 cm as centre. (Use a = 22 and 13 = 1.73).
​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Area of equilateral triangle =

$\frac{ \sqrt{3 {a}^{2} } }{4} \\ = \frac{ \sqrt{3} }{4} \times 14 \times 14 \\ = \frac{196 \sqrt{3} }{4} \: \: = 49 \sqrt{3} \\ = 49 \times 1.73 \\ = 84.77 \: {cm}^{2}$

Area of the circle =

$= \pi {r}^{2} \\ = \frac{22}{7} \times 7 \times 7 \\ = 154 \: \: {cm}^{2}$

Area of sector =

$= \frac{thetha}{360} \times \pi {r}^{2} \\ = \frac{60}{360} \times \frac{22}{7} \times 7 \times 7 \\ = 25.66 {cm}^{2}$

Area of shaded region = ( Area of circle -

Area of sector) + Area of triangle

= (154 - 25.66) + 84.77

= 128.34 + 84.77

= 213.11 cm^2

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