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Let $ABCDEF$ be a regular hexagon and $P$ and $Q$ be the midpoints of $AB$ and $CD$, respectively. Then, the ratio of the areas of trapezium $PBCQ$ and hexagon $ABCDEF$ is

A regular octagon ABCDEFGH has sides on length 6 cm each. Then the area, in sq. cm, of the square ACEG is

In a regular polygon, any interior angle exceeds the exterior angle by $120$ degrees. Then, the number of diagonals of this polygon is

Regular polygons $A$ and $B$ have number of sides in the ratio $1: 2$ and interior angles in the ratio $3: 4$. Then the number of sides of $B$ equals

If the area of a regular hexagon is equal to the area of an equilateral triangle of side $12$ cm , then the length, in cm , of each side of the hexagon is

Suppose the length of each side of a regular hexagon $ABCDEF$ is $2$ cm. It $T$ is the mod point of $CD$, then the length of $AT$, in cm, is

Let $A$ and $B$ be two regular polygons having $a$ and $b$ sides, respectively. If $b = 2a$ and each interior angle of $B$ is $3/2$ times each interior angle of $A$, then each interior angle, in degrees, of a regular polygon with $a + b$ sides is

Corners are cut off from an equilateral triangle $T$ to produce a regular hexagon $H$. Then, the ratio of the area of $H$ to the area of $T$ is

Let $ABCDEF$ be a regular hexagon with each side of length $1$ cm. The area (in sq cm) of a square with $AC$ as one side is