Areas of Combination of Plane Figures

Q.

Find the area of the shaded portion in the figure if the diameter of the larger circle is 12 cm.

1. 70.71 cm²

2. 69.43 cm²

3. 82.53 cm²

4. 88.53 cm²

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

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

Q.

In the given figure, a circle is inscribed in a trapezium of height 14 cm and lengths of parallel sides are equal to 25 cm and 40 cm. What is the area of the shaded region?

1. 154 sq cm
2. 301 sq cm
3. 509 sq cm
4. 455 sq cm

Q.

In the diagram, a square is drawn such that the diagonally opposite corners touch the Centre and the circumference of a circle whose radius is r. Find the area of the square.

1. $\frac{r^2}{4}$

2. $2r^2$

3. $r^2$

4. $\frac{r^2}{2}$

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. 4
3. 2
4. 3

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.

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. 3, 2, 1

3. 2, 1, 3

4. 2, 3, 1

Q.

A stadium is in circular shape. Within the stadium some areas have been allotted for a hockey court and a javelin range, as given in the figure. Assume the shape of the hockey court and the javelin range to be square and triangle, resp. The curators would like to accommodate a few more sports in the stadium. Help them by measuring the unallocated region within the stadium.(the radius of the stadium is 200 mts.)

1. 22853.14 m²

2. 22857.14 m²

3. 20000 m²

4. 62857.14 m²

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