Areas of Combination of Plane Figures

Q.

Question 15
In Fig. 12.33, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.

Q. 57.A triangle ABC is divided into four regions by three lines parallel to BC. The lines divided AB into four equal segments. If the second largest region has area 25, what is the area of ABC?

Q. Question 6
For going to a city B from city A, there is a route via city C such that AC $\perp$ CB, AC = 2x km and CB = 2(x+7) km. It is proposed to construct a 26 km highway which directly connects the two cities A and B.Ffind how much distance will be saved in reaching city B from city A after the construction of the highway.

Q.

The area of a trapezium is 126 sq. cm. The height of the trapezium is 14 cm. If one of its parallel sides is 8 cm longer than the other side, find the lengths of the parallel sides.

1. 4 cm, 12 cm

2. 5 cm, 13 cm

3. 6 cm, 14 cm

4. 3 cm, 11 cm

Q.

The figure shows the cracker and the circle formed by the sparkles of the cracker. Find the area of the ground it covered if the sparkle formed was of 28 cm from the cracker.

1. 2156 cm²

2. 2464 cm²

3. 4258 cm²

4. 4259 cm²

Q.

On a square handkerchief of side 50 cm, seven non-intersecting circles designs of each radius 7 cm are made. Find the area of the remaining portion of the handkerchief in $c{m}^2$.

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Q. The base of triangular field is three times its height. If the cost of cultivating the field at Rs. $36.72$ per $100$ $m^2$ is Rs. $49,572$; find its base and height.

1. Base $600$ m, height = $300$ m
2. Base $800$ m, height = $300$ m
3. Base $400$ m, height = $300$ m
4. Base $900$ m, height = $300$ m

Q. from a circular canvas of diameter 56m a sector of 270^° was cut out and a conical tent was formed by joining the straight ends of this piece. find the radius and height of ten

Q.

In figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region (in $c{m}^2$).

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Q.

In the figure a small square is inserted inside the bigger square. The area of the shaded region of the square is__ sq.cm.

Q. From each of the two opposite corners of a square of side $8$ cm, a quadrant of a circle of radius $1.4$ cm is cut. Another circle of radius $4.2$ cm is also cut from the centre as shown in Fig. Find the area of the remaining (shaded) portion of the square. (Use $\pi$ $=\frac{22}{7}$).

Q.

Find the area of shaded region in the given fig. where ABCD is a square of side 10 cm and semi-circles are drawn with each side of square as diameter. [$\pi =3.14$]

Q. Find the area and the perimeter of a semi-circle of radius 7 cm.

Q. The ratio of the area of a square inscribed in a semi-circle to that of the area of a square inscribed in the circle of the same radius is:

1. $2:1$
2. $2:5$
3. $1:3$
4. $2:3$

Q. $ABCP$ is a quadrant of a circle of radius $14cm$. With $AC$ as diameter, a semicircle is drawn. Find the area of the shaded portion.

1. $47c{m}^2$
2. $72c{m}^2$
3. $98c{m}^2$
4. None of these
   

Q. The figure shows a circle with center O and diameter PQ. Point R lies on the circumference of the circle such that PR=QR and PR= 4 cm.The radius of the given circle (correct to two decimal places) is

1. 2.83 cm
2. 4cm
3. 2cm
4. 8cm

Q.

A circular garden has a water body which is in the shape of a circle with diameter 14 m.The remaining part of the garden is covered with grass and this portion is 7 m wide. Find the area of the lawn in $m^2$

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Q. Question 2
Write True or False and justify your answer :
PQRS is a rectangle inscribed in a quadrant of a circle of radius 13 cm and A is any point on PQ. If PS = 5 cm. Then, ar ($\Delta$PAS)= $30c{m}^2$.

Q. $ABC$ is a quadrant of a circle of radius $14$ $cm$ and a semicircle is drawn with $BC$ as diameter. Find the area of the shaded region.

Q. If $a^2+\frac{1}{a^2}=18$ where $a\ne 0$; then find $a^3-\frac{1}{a^3}$

1. $\pm 70$
2. $\pm 74$
3. $\pm 72$
4. $\pm 76$

Q. In the adjoining figure, $ABC$ is a right angled triangle right angled at $A$. semi-circle are drawn on AB, AC and BC as diameters. find the area of the shaded region.

1. $6.5c{m}^2$
2. $7c{m}^2$
3. $6c{m}^2$
4. $4c{m}^2$

Q. Four horses are tied on the four corners of a square field of $14m$ length so that each horse can just touch the other two horses. They were able to graze in the men accessible to them for $11$ days. For how many days is the ungrazed area sufficient for them?

1. 3 days
2. 4 days
3. 5 days
4. 2 days

Q. ABCD is a trapezium in which $AB\parallel CD$. Then ${AC}^2+{BD}^2$ is equal to:

1. ${AD}^2+{BC}^2-2AB.CD$
2. ${AD}^2+{BC}^2+2AB.CD$
3. ${AD}^2-{BC}^2+2AB.CD$
4. ${AD}^2-{BC}^2-2AB.CD$

Q. Plane Geometry
The straight line, which is parallel to the base of a triangle, divides its area in half. In what ratio does it divide its lateral sides?

Q. In the given figure, the area of the shaded portion is __________.

1. $308c{m}^2$
2. $462c{m}^2$
3. $154c{m}^2$
4. $150c{m}^2$

Q. In the figure above, $O$ is the centre of the circle with diameter $10$. Find the length of minor arc $XY$, if the area of the shaded region is $\pi$

1. $\frac{4\pi }{5}$
2. $5\pi$
3. $\frac{5\pi }{2}$
4. $\frac{2\pi }{5}$

Q.

In the given figure, you see the frame of a lampshade. It is to be covered with a decorative cloth. The frame has a base diameter of 20 cm and height of 30 cm. A margin of 2.5 cm is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade.

Q.

Question 8 (ii)

The figure depicts a racing track. ADHE is a semicircular track of inner radius 30m and thickness 10m. FGBC is another semicircular track with the same inner radius and thickness as ADHE. The space between the two semicircular tracks are covered by straight tracks of length 106m and thickness 10m on either side. Calculate the area of the racing track.

Q.

OACB is a quadrant of a circle with centre O and radius 7 cm. It OD = 4cm, then find area of shaded region.

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Q. Is it true to say that area of a segment of a circle is less than the area of its corresponding sector? Why?

1. yes, it is true for minor segment since ar.minor segment $=$ ar.sector-triangle made by the radii and the chord of the segment.
2. Yes, it is only true for major segment since ar.minor segment $=-$ ar.sector-triangle made by the radii and the chord of the segment
3. No, it is only true for major segment since ar.minor segment
   =ar.sector-triangle made by the radii and the chord of the segment.
4. No, it is only true for minor segment since ar.minor segment
   =ar.sector-triangle made by the radii and the chord of the segment.