Question

The area of an equilateral triangle

inscribed in a circle is 4√ 3 cm2

.

The area of the circle is
?​

Answer 1

$\star$ Answer :

$\star$ Area of the circle = $\frac{16\pi }{3}cm^2$

$\star$ Step-by-step explanation :

$\star$ Given , Area of equilateral triangle = $\frac{\sqrt{3} }{4}a^2$ = $4\sqrt{3}cm^2$

Where, a is side of equilateral triangle.

=>  $\frac{\sqrt{3} }{4}a^2$ = $4\sqrt{3}$

=> a² = 16

$\star$ => a = ± 4

$\star$ But a can't be negative .

$\star$ So , a = 4 cm.

From, figure (In attachment) ,

$\star$ BD = 1/2*(a) = 2 m and

$sin60=\frac{opp.side}{hypotenuse}=\frac{BD}{Radius}\\\\=>sin60=\frac{2}{R}\\\\ =>R=\frac{4}{\sqrt{3} }$

$\star$ Since , sin 60 = √3 / 2

$\star$ Now , The area of circle = $\pi R^2$

$=>\pi *(\frac{4}{\sqrt{3} } )^2\\\\=>\frac{16\pi }{3} cm^2$

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