Areas of Combination of Plane Figures

Q. It is proposed to build a single circular park equal in area to the sum of areas of two circular park of diameter 16 m and 12 m in a locality. The radius of the new park would be 15 m.

Q. Find the area of right angled triangle if the radius of its circum-circle is 5cm and the altitude drawn to the hypotenuse is 4cm

Q.

Question 79

Find the area of the shaded portion in the following figure.

Q.

Given below is a semicircle of diameter 12cm which encloses two other semicircles. Find the area of shaded region.

1. 30

2. 16

3. 21.9

4. 28.24

Q.

Consider the following steps. Which would be the correct order to solve the above-mentioned question?
1. Find the area of each unshaded region.
2. Identify the unshaded regions.
3. Subtract the sum total of areas of unshaded regions from the area of the square.

1. 2, 1, 3

2. 3, 2, 1

3. 2, 3, 1

4. 1, 2, 3

Q.

A circular pond is $17.5m$ is of diameter. It is surrounded by a $2m$ wide path. Find the cost of constructing the path at the rate of $Rs25per{m}^2$

Q.

4 focus lights are to be fixed on a square aluminum plate with side length, l = 28 inch. Circles are cut in the plate to accommodate the lights. After the required alterations the aluminum plate looks similar to the figure shown. What would be the area of the aluminum plate after alterations?

1. 169 sq inches

2. 168 sq inches

3. 180 sq inches

4. 200 sq inches

Q.

A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is 84 cm and length is 1 m.

Q.

What will be the cost for surfing a square water tank with sides 20 m surrounded by four semi-circular grassy plots, given that cost for surfing per m² is Rs.2.5?

1. 1570

2. 2000

3. 3140

4. 840

Q. A circle with radius $7cm$ is drawn inside a rhombus with diagonals $21cmand32cm$. Find the area of the shaded region.

1. 182$c{m}^2$
2. 180$c{m}^2$
3. 181$c{m}^2$
4. 183$c{m}^2$

Q. Each side of an equilateral triangle is $a$ cm. Find out the ratio of areas of the circumcircle and the incircle of the triangle:

1. 1 : 2
2. 2 : 1
3. 4 : 1
4. 1 : 4

Q. The perimeter of a triangle is $24cm$. The length of the its sides are consecuctive integer. Find its sides.

Q.

The area of an equilateral $\Delta ABC$ is 17320.5 $c{m}^2$ with each vertex of the triangle as centre a circle is drawn with radius equal to half the length of the side of triangle. Find the area of the shaded region. $(\pi =3.14,\sqrt{3}=1.73205)$ [4 MARKS]

Q.
The area of the shaded region in the given figure is sq $\text{in. [ Take π =}\frac{22}{7}]$

1. 10.5
2. 11.5
3. 10
4. 11

Q. A circular field of radius $105$ m has a circular path of uniform width of $5$ m along and inside its boundary. Find the area of the path.

Q.

Area of the shaded region in the figure shown above is

1. Area of sector CMN + Area of sector COP

2. Area of sector COP + Area of sector CMN

3. Area of quadrilateral MNOP – Area of sector CMN

4. Area of sector COP - Area of sector CMN

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.

A large circular farm is next to a river. A farmer can fence the farm with an iron wire of length 18.84 m. How much area will be enclosed by the fence (in $m^2)$?

1. 29.28

2. 28.26

3. 26.28

4. 28.29

Q.

The area of the colored region in the figure will be = (Area of X) (Y) (Area of Z). Identify X, Y and Z.

1. ABCD + PQRS

2. PQRS - ABCD

3. ABCD - PQRS

4. PQRS + ABCD

Q. Find the area of the shaded region in the figure shown.

Q. If $2\frac{1}{x}\times 4\frac{1}{2}=10\frac{1}{2}$, then the value of '$x$' is-

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

Q. The area of triangle ACD in the given figure is 90 sq. ft

1. True
2. False

Q.

A large circular farm is next to a river. A farmer can fence the farm with an iron wire of length 18.84 m. How much area will be enclosed by the fence (in $m^2)$?

1. 29.28

2. 28.26

3. 26.28

4. 28.29

Q. Calculate the area and the perimeter of a circle of it diameter is 12cm