Radius of a circle inscribed in a regular hexagon is 24 c.m. then find the length of hexagon
To find the length of a regular hexagon when the radius of a circle inscribed in it is given, we can use the formula:
Length of hexagon = 2 * radius * tan(π/6)
In this case, the radius of the circle inscribed in the regular hexagon is given as 24 cm. Let's substitute this value into the formula:
Length of hexagon = 2 * 24 cm * tan(π/6)
Now, we need to find the value of tan(π/6). To do that, we can use a calculator or refer to the trigonometric values of special angles. The value of tan(π/6) is √3/3.
Substituting this value into the formula:
Length of hexagon = 2 * 24 cm * (√3/3)
Simplifying further:
Length of hexagon = 48 cm * (√3/3)
To represent the answer as a simplified radical, we multiply 48 by √3 which gives:
Length of hexagon = 48√3 cm
Therefore, the length of the hexagon is 48√3 cm.