Polygons

The regular pentagon $ABCDE$ is inscribed in a circle with the center $S$ (see the picture). Give the measure of the angle $ASB$.

In the regular hexagon $ABCDEF$, $G$ and $H$ are the midpoints of $AB$ and $CD$. What part of the area of the hexagon is covered by the area of the quadrilateral $BCHG$? The area of the quadrilateral corresponds to the shaded region in the figure.

$ABCDEF$ is a regular hexagon. (See the picture.) The area of the triangle $ABC$ is $6{\mathrm{cm}}^2$. Calculate the area of the hexagon.

A regular pentadecagon ($15$ sided polygon) is inscribed in a circle of radius $8\mathrm{cm}$. Calculate its area. Round the result to two decimal places.