Advertisement Remove all ads

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) 

Advertisement Remove all ads

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 

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

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

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

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×