Areas of Combination of Plane figures

Q. In the first figure, ABCD is a rhombus with diagonals of length 6 cm and 8 cm respectively. The circle inscribed in the rhombus is of radius 2.4cm. The second figure shows a parallelogram EFGH with EF = GH = 6 cm and the perpendicular distance between EF and GH is 4 cm. $\angle$EFG = $\angle$EHG = 120 degrees. Two arcs are drawn with centres as F and H, with radii 2.4 cm. The area of shaded region in figures 1 and 2 are equal. State true or false.

1. True
2. False

Q. The number of regions that have the area equal to the areas of regions I and II put together will be:

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

Q. How would you go about finding the area of the shaded region?

1. (Area of I + Area of III) + (Area of II + Area of IV)
2. (Area of I + Area of IV) + (Area of II + Area of III)
3. (Area of I + Area of II) $\times$ 2
4. (Area of I + Area of II) + (Area of III + Area of IV)

Q.

The area of an equilateral $\Delta$ABC is 17320.5 $c{m}^2$. A circle is drawn taking the vertex of the triangle as centre. The radius of the circle is half the length of the side of triangle. Find the area of the shaded region (in $c{m}^2$) . ($\pi$ = 3.14 , $\sqrt{3}$ =1.73205)

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Q.

How many tiles whose length and breadth are $12cmand5cm$ respectively will be needed to fit in a rectangular region whose length and breadth are $70cmand36cm$ respectively?

Q.

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

Q. Find the areas(in $c{m}^2$) of shaded regions. [Take $\pi =\frac{22}{7}$]

1. $\frac{49}{2}$
2. $\frac{35}{2}$
3. $\frac{119}{4}$

Q. The areas of the region shaded in blue in the given figures are equal.

1. False
2. True

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. 1, 2, 3

2. 2, 1, 3

3. 3, 2, 1

4. 2, 3, 1

Q. What will be the angle in each sector that is to be considered?

1. ${30}^{\circ }$
2. ${90}^{\circ }$
3. ${45}^{\circ }$
4. ${60}^{\circ }$

Q. The area between two concentric circles of radii $r_1$ and $r_2,$ is equal to [$r_2>r_1$]

1. zero
2. $\pi r_1^2$
3. $\pi r_2^2$
4. πr22-πr12

Q. How would you find the area of the shaded region?

1. Area of the square - Area of quarter circle
2. Area of square + Area of quarter circle
3. Area of square - (4 $\times$ Area of one quarter circle)
4. Area of square + (4 $\times$ Area of quarter circle)

Q.

State true or False.
Areas of the shaded regions in figures 1 and 2 are equal. The corresponding lengths and breadths of the rectangles are equal, and the radius of the quarter circles in figure 1 is half the breadth of the rectangle.

1. False

2. True

Q.
Compare area of region I and II.

1. Area of region I = Area of region II
2. Area of region I > Area of region II
3. Area of region I < Area of region II
4. Area of region I = 2$\times$Area of region II