Areas of Combinations of Plane Figures

In the figure below, $XPY$ is a semi-circle whose diameter $XY=18 \mathrm{cm}$ and its centre is $R$. 

What is the area of the shaded region?

In the figure below, $PQRS$ is a square, $O$ is the centre of the circle. If $RS=10\sqrt{2}$ unit, then area of the shaded region is

A right-angled isosceles triangle is inscribed in a circle of radius $r$. What is the area of the remaining portion of the circle?

The figure shows a circle which has a diameter $\mathrm{AB}$ and a radius $13$. If chord $\mathrm{CA}$ is $10 \mathrm{cm}$ long, then find the area of $△\mathrm{ABC}$.

In the given figure, $ABC$ is an equilateral triangle inscribed in a circle of radius $8 \mathrm{cm}$. Area of the shaded portion will be

A square is circumscribing a circle. The side of the square is $14 \mathrm{cm}$. Find the area of the square not included in the circle.

A square is circumscribing a circle. The side of the square is $14$cm. The area of the square not included in the circle is

$AB, CD$ and $EF$ are the arcs of the three concentric circles with radius $21 cm, 14 cm$ and $7 cm$ respectively with centre $O$ as shown in the figure. If $\angle AOB=60°$, then the sum of the areas of two shaded regions are:

Consider the approximate value of$\mathrm{\pi }$ as $\frac{22}{7}$.

Find the area of shaded portion in the figure given below, where $ABCD$ is a square of side $28 \mathrm{cm}$:

A person has a rectangular sheet of metal. He has to make cylindrical vessel whose both circular ends are closed. When he minimize the wastage of the sheet, then what is the ratio of the wasted sheet to the utilized sheet? $\left(\mathrm{\pi }=\frac{22}{7}\right)$

Find the area of the shaded region if three equal circles of $1$ cm radius touching externally as shown are drawn inside a regular hexagon.

ABCD is a rectangle. D as a centre a quarter circle is drawn inside the rectangle and touches the semicircle drawn on AB as diameter at F. Find the area of shaded region if AB$=2$ units.

A set of circles are drawn in a square of side of $12$ units as shown in diagram. Find the area of the shaded region (sq. units).

A semicircle is drawn on one side of the right-angled isosceles ABC right-angled at A. Find the area of the shaded region if AC$=6$cm.

$\angle$ABC$=30°$,  AB$=2\sqrt{6}$ . What is the area of the shaded region?

O is the center of the circle which circumscribes a square of length equal to $2$ cm for semicircles are drawn with a side of the square as diameter. Find the area of the shaded region.

Find the area of the shaded region of the circle with O as center and OABC is a square with side $6$ cm.

 

AB, BC and AC are the diameter of three mutually touching semicircles. DE is common tangent. Find area of shaded region if DE$= 4\sqrt{3}$cm in length.

ABCD is a trapezium inscribed in a semicircle with PQ as diameter. If PA$=4$, AB$=14$, BQ$=2$ DA$\perp$PQ, CB$\perp$PQ, then what is the area of the shaded portion?

If the radii of the circles is $1.5$ and $4.5$ units and AB is a common tangent then find the area of the shaded region.