面積與體積

The figure shows a regular pentagon. Find its area correct to the nearest $0.01\text{ cm}^2$.

In the figure, a solid right circular cone of height $12\text{ cm}$ is put into a cylinder which has the same internal radius as the base radius of the cone. Water is then poured into the cylinder until the water level just reaches the tip of the cone. If the cone is removed, what is the height of the water in the cylinder?

In the figure, $OABC$ is a sector. Find the length of the arc $ABC$.

In the figure, $A$, $B$ and $C$ are the centres of three equal circles, each of radius $1\text{ cm}$. Find the area of the shaded region.

In the figure, a square of side $x$ cm is cut into $9$ equal squares. If the total perimeter of the $9$ small squares is $72$ cm more than the perimeter of the original square, then $x=$

The figure shows a trapezium of area $6\text{ cm}^2$. Find $x$.

In the figure, $ABCD$ is a rectangle formed by four squares each of area $1\text{ cm}^2$. $DB$ is a diagonal. Find the area of the shaded region.

In the figure, $PXQ$, $QYR$ and $RZP$ are semicircles with areas $A_1\text{ cm}^2$, $A_2\text{ cm}^2$ and $A_3\text{ cm}^2$ respectively. If $A_1=12$ and $A_2=5$, find $A_3$.

In the figure, $CAB$ is a semicircle and $ABCD$ is a parallelogram. Find the area of $ABCD$.

The figure shows a square, a triangle and a sector with areas $a\text{ cm}^2$, $b\text{ cm}^2$ and $c\text{ cm}^2$ respectively.

Which of the following is true?