# A regular hexagon is inscribed in a circle. If the area of hexagon is 24 √ 3 , find the area of the circle. (Use π = 3.14) - Mathematics

Sum

A regular hexagon is inscribed in a circle. If the area of hexagon is $24\sqrt{3}$ , find the area of the circle. (Use π = 3.14)

#### Solution

Let the radius of the circle be r and side of hexagon be a.
Area of hexagon =$\frac{3\sqrt{3}}{2} a^2$

$\Rightarrow 24\sqrt{3} = \frac{3\sqrt{3}}{2} a^2$
$\Rightarrow a^2 = 16$
$\Rightarrow a = 4 cm$

In an regular hexagon inscribed in a circle, its side is equal the radius.
∴ r = a = 4 cm
Now, Area of circle is given by

$\pi r^2$
$= 3 . 14 \times 4 \times 4$
$= 50 . 24 {cm}^2$

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 13 Areas Related to Circles
Exercise 13.4 | Q 28 | Page 60