[ Linear dependence of vectors ]  [ Angles between lines and planes ]

The side of the base and the height of a regular hexagonal pyramid are equal to $a$. Find the radius of the sphere circumscribed around the pyramid.
Let $A B C D E F P$ be a given regular hexagonal pyramid with vertex $P, A B=B C=C D=D E=E F=A F$ $=a, M$ - the center of the regular hexagon $A B C D E F$. Since the pyramid is regular, $P M$ is its height, and since by condition $P M=a$, the point $M$ is equidistant from all vertices of the pyramid $A B C D E F P$. Therefore, $M$ is the center of the sphere circumscribed around the pyramid $A B C D E F P$. Consequently, the radius of this sphere is $a$.

## Answer

$a$.