Areas of Combination of Plane Figures

Q.

Find the perimeter of the shaded region in the figure, if ABCD is a square of side 14 cm and APB and CPD are semicircles.

Q.

Find the area of the shaded region in the given figure, where a circular arc of radius 6 cm has been drawn with vertex of an equilateral triangle of side 12 cm as centre and a sector of circle of radius 6 cm with centre B is made. [ Use $\sqrt{3}=1.73and\pi =3.14$.]

Q. Due to heavy floods in a state, thousands were rendered homeless. 50 schools collectively offered to the state government to provide place and the canvas for 1500 tents to be fixed by the government and decided to share the whole expenditure equally. The lower part of each tent is cylindrical of base radius 2.8 m and height 3.5 m, with conical upper part of same base radius but of height 2.1 m. If the canvas used to make the tents costs Rs 120 per sq. m, find the amount shared by each school to set up the tents. What value is generated by the above problem ? (Use $\pi =\frac{22}{7}$)

Q.

Question 6
In a circular table cover of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in Fig. 12.24. Find the area of the design.

Q.

In the given figure, $△ABC$ is right-angled at A. Find the area of the shaded region if AB = 6 cm, BC = 10 cm and O is the centre of the incircle of $△ABC$. [Take $\pi$ = 3.14 ]

Q.

In the given figure, $△ABC$ is right-angled at A. Semicircles are drawn on AB, AC and BC as diameters. It is given that AB = 3 cm and AC = 4 cm. Find the area of the shaded region.

Q.

$AB$ and $CD$ are respectively arcs of two concentric circles of radii $21cm$ and $7cm$ and centre $O$. If $\angle AOB={30}^{\circ }$, find the area of the shaded region.

Q.

In the given figure, O is the centre of the bigger circle, and AC is its diameter. Another circle with AB as diameter is drawn. If AC = 54 cm and BC = 10 cm, find the area of the shaded region.

Q.

PQRS is a diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal. Semicircles are drawn with PQ and QS as diameters, as shown in the given figure. If PS = 12 cm, find the perimeter and area of the shaded region. [ Take $\pi$ = 3.14]

Q.

The length of a minute hand of a wall clock is 7 cm. What is the area swept by it in 30 minutes

1. 50 cm²

2. 35 cm²

3. 77 cm²

4. 63 cm²

Q.

The inside perimeter of a running track (shown) is 400 m. The length of each of the straight portion is 90 m and the ends are semi-circles. If the track is everywhere 14 m wide, find the area of the track. Also, find the length of the outer running track.

Q.

The area of the largest triangle that can be inscribed in a semi-circle of radius ‘r’ is:

1. $r^2$

2. $2r^2$

3. $\frac{1}{2}{r}^2$

4. $r^3$

Q.

Four equal circles are described about the four corners of a square so that each touches two of the others, as shown in the figure. Find the area of the shaded region, if each side of the square measures 14 cm.

Q.

In the given figure, the side of square is 28 cm and radius of each circle is half of the length of the side of the square, where O and O' are centres of the circles. Find the area of shaded region.

Q.

In the given figure, O is the centre of the circle with AC = 24 cm, AB = 7 cm and $△$ BOD = 90${}^{\circ }$. Find the area of shaded region.

[Use $\pi$ = 3.14]

Q.

A cone has ………. curved face and ……… flat face.

Q.

In the given figure, APB and CQD are semicircles of diameter 7 cm each, while ARC an BSD are semicircles of diameter 14 cm each. Find the (i) perimeter, (ii) area of the shaded region.

Q.

Find the area enclosed between two concentric circles of radii 3.5 cm and 7 cm. A third concentric circle is drawn outside the 7 cm circle, such that the area enclosed between it and the 7 cm circle is same as that between the two inner circles. Find the radius of the third circle correct to one decimal place.

Q.

PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA & PB are perpendicular to each other, then the length of each tangent is:

1. 3 cm

2. 4 cm

3. 5 cm

4. 6 cm

Q. Find the area of the shaded region in the given figure, if ABCD is a square of side 20 m and APD and BPC are semicircle.

Q.

In a circle of radius 7 cm, a square ABCD is inscribed. Find the area of the circle which is outside the square.

Q.

In Fig. the square ABCD is divided into five equal parts, all having same area. The central part is circular and the lines AE, GC, BF and HD lie along the diagonals AC and BD of the square. If AB = 22 cm, find:

Q.

In the given figure, PQ = 24 cm, PR = 7 cm and O is the centre of the circle. Find the area of the shaded region. [Take $\pi =3.14$]

Q.

In the given figure, two concentric circles with centre O have radii 21 cm and 42 cm. If $\angle$AOB = 60 ${}^{\circ }$, find the area of the shaded region. [ Use $\pi$ = \frac{22}{7}.]

Q.

In the given figure, ABCD is a square of side 7 cm, DPBA and DQBC are quadrants of circles each of the radius 7 cm. Find the area of shaded region.

Q.

ABCD is a rectangle, having AB = 20 cm and BC = 14 cm. Two sectors of ${180}^{\circ }$ have been cut off. Calculate

(i) The area of the shaded region

(ii) The length of the boundary of the shaded region.

Q.

Sum of the sides of a polygon is called __ of the polygon.

Q.

Question 13
In Fig. 12.31, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. $(Use\pi =3.14)$

Q.

In Fig. the boundary of the shaded region consists of four semi-circular arcs, the smallest two being equal. If the diameter of the largest is 14 cm and of the smallest is 3.5 cm, find

(i) The length of the boundary

(ii) The area of the shaded region.

Q.

A rectangular park is 100 m by 50 m. It is surrounded by semi-circular flower beds all round. Find the cost of levelling the semi-circular flower beds at 60 paise per square metre. (Use $\pi =3.14$)