Hexagon Side and Circumscribing Circle Radius
A regular hexagon can be divided into 6 equilateral triangles, with the center of the hexagon being a common vertex. The side length of each equilateral triangle is equal to the side length of the hexagon, denoted as $a$. The radius ($r$) of the circle that circumscribes the hexagon is the distance from the center to any vertex.
In a regular hexagon, this distance (the radius $r$) is equal to the side length of the hexagon.
- Radius of the circumscribing circle, $r = a$.
Calculating Circle Area
The formula for the area ($A$) of a circle is given by:
$A = \pi r^2$
Substitute the radius $r = a$ into the area formula:
$A = \pi (a)^2$
$A = \pi a^2$
Therefore, the area of the circle that circumscribes a regular hexagon with side $a$ is $\pi a^2$.
Important Questions from Geometry (Notes)
- In a triangle PQR, if $\angle P + \angle R = 150^\circ$ and $\angle P + 3\angle Q = 170^\circ$, then $\angle P$ is equal to :
- PQR is a triangle. The bisectors of the internal angle $\angle Q$ and external angle $\angle R$ intersect at M. If $\angle QMR = 40^\circ$, then $\angle P$ is :
- A $2\text{ m}$ long ladder is to reach a wall of height $1.75\text{ m}$. The largest possible horizontal distance of the ladder from the wall could be
A, B, C, D are points on a circle with AB=5 cm, BC=12 cm, AC=13 cm and AD=7cm. Then, the closest approximation of CD is
- An inclined plane rests against a horizontal cylinder of radius $R$. If the plane makes an angle of $30^\circ$ with the ground, the point of contact of the plane with the cylinder is at a height of
