Polygons(n>3)

Q. ABCD is a rectangle of dimensions 6 cm $\times$ 8 cm. DE and BF are the perpendiculars drawn on the diagonal of the rectangle. What is the ratio of the shaded to that of unshaded region?

1. 7 : 3
2. 16 : 9
3. Data insufficient
4. $4:3\sqrt{2}$

Q.

Two trains, one from A to B and the other from B to A, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 25 hours respectively. The ratio of their speeds is:

1. 5:3

2. 2:3

3. 6:7

4. 1:5

Q.

The perimeter of a square and a circular field are same. If the area of the circular field is 3850 sq.m, then area of the square is -

1. 4225 m²

2. 2050 m²

3. 3025 m²

4. 2650 m²

5. 2750 m²

Q.

What is a $50$ sided shape called?

Q.

The sum of the squares of three consecutive natural numbers is 2030.What is the middle number?

1. 25

2. 26

3. 27

4. 28

5. 24

Q. What is the sum of all the angles of a 9 pointed star $(i.e.,\angle 1+\angle 2+\angle 3+\dots \angle 8+\angle 9)$:

1. ${909}^{\circ }$
2. ${540}^{\circ }$
3. ${720}^{\circ }$
4. ${900}^{\circ }$

Q. In the figure, ABCD is a square with side 10. BFD is an arc of a circle with centre C. BGD is an arc of a circle with centre A. What is the area of the shaded region?

1. $100-50\pi$
2. $100-257\pi$
3. $50\pi -100$
4. $25\pi -100$

Q.

A rectangle is divided into four rectangles, and their respective areas are shown in the figure. (Figure is not drawn to scale). What is the missing area 'X' of the fourth rectangle?

$\begin{array}{cc}25& 20\\ 5& x\end{array}$

1. 2sq units

2. 4sq units

3. 2.5 sq units

4. 5sq units

Q.

Area of a regular hexagon having side length as 2 cm is -

1. 8 √3 cm²

2. 5 √3cm²

3. 7 √3 cm²

4. 4 √3 cm²

5. 6 √3 cm²

Q.

The adjacent sides of a rectangle with a given perimeter is $100\text{cm}$ and enclosing maximum area are.

1. $10\text{cm and}40\text{cm}$

2. $20\text{cm and 3}0\text{cm}$

3. $25\text{cm and}25\text{cm}$

4. $15\text{cm and}35\text{cm}$

Q. In the figure given below, ABCD is a rectangle. The area of the isosceles right triangle , $ABE=7c{m}^2$ EC= 3BE. The area of ABCD $\left(inc{m}^2\right)$ is:___

Q. ABCD is a square, in which a circle is inscribed touching all the sides of square. In the four corners of the square, 4 smaller circles of equal radii are drawn, containing the maximum possible area. What is the ratio of the area of the larger circle to that of the sum of the areas of four smaller circles?

1. $Noneofthese$
2. $1:(68-48\sqrt{2})$
3. $1:17\sqrt{2}$
4. $3:(34-12\sqrt{2})$

Q.

$\text{If the side of square is}\frac{1}{2}(x+1)\text{and its diagonal is}\frac{3-x}{\sqrt{2}}\text{units, find the length of a side of the square.}$

1. 3

2. 4

3. 1

4. 2

5. 5

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 : 3
2. 2 : 1
3. 2 : 5
4. None of these

Q. ABCD is a trapezium in which AB is parallel to DC, AD = BC, AB = 6 cm, AB = EF and DF = EC. If the area of ABEF is half of ABCD, then find DF/CD.

1. 1/3
2. 1/4
3. 2/5
4. 1/6

Q.

If three numbers in the ratio 3 : 2: 5 be such that the sum of their squares is 1862, the middle number will be

1. 7

2. 14

3. 28

4. None

Q. If the area of a pair of diagonally opposite triangles (Formed by joining the diagonals of the quadrilateral) is 12 and 27 respectively, then the minimum area of quadrilateral ABCD is ___

Q.

The ratio of squares of first n natural numbers to square of sum of first n natural numbers is17:325. The value of n is:

1. 24

2. 25

3. 20

4. 26

5. none

Q.

If the ratio of angles of a hexagon is 1:2:3:5:6:7, find the measure of smallest angle.

1. 70⁰

2. 50⁰

3. 60⁰

4. 30⁰

Q. In the given figure, EFGH is formed by joining midpoints of consecutive sides of square ABCD. Figures PQRS and KLMN are also formed similarly. KLMN : ABCD is

1. 1 : 4
2. 1 : 16
3. 1 : 8
4. None of the above

Q. The figure below shows two concentric circles with centre O. PQRS is a square inscribed in the outer circle. It also circumscribes the inner circle, touching it at point B, C, D and A, What is the ratio of the perimeter of the outer circle to that of polygon ABCD?

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

Q.

A park has the shape of a regular hexagon of sides 2 m each. Ram walks a distance of 5 m around the perimeter. What is the direct distance between the start point and the end point?

1. 

2. 
   

3. 
   

4. 
   

Q. A trapezium DEFG is circumscribed about a circle that has centre C and radius 2 cm. If DE = 3 cm and the measure of $\angle$DEF=$\angle$EFG=90${}^{\circ }$, then find the area of trapezium DEFG

1. 18 cm²
2. 16 cm²
3. 15 cm²
4. 20 cm²

Q. All sides of a regular pentagon are extended to form a star with vertices P, Q, R, S, T. What is the sum of the angles made at the vertices?___

Q. In the given figure, ABCD is a rectangle with length as 2 and breadth as 1. The area of rectangle BDFE is:

1. $2$
2. $\sqrt{5}$
3. $\sqrt{2}$
4. $1+\sqrt{2}$

Q. Two rectangles, ¨ABCD and ¨PQRS overlap each other as shown in the figure below. Also, the overlapped area (shaded region) is 20% ¨ABCD and 33.8% of ¨PQRS. If the ratio of corresponding sides of the two rectangles is same is then ratio AD : PR equals

1. none of these
2. 1.2
3. 1.5
4. 1.6

Q.

Area of a regular octagon of side length $\sqrt{2}$ cm is -

1. 2 ( √2 + 1 ) cm²

2. 3 ( √2 + 1 )cm²

3. ( √2 + 1 )cm²

4. 4( √2 + 1 ) cm²

Q. In the given figure, EADF is a rectangle and ABC is a triangle whose vertices lie on the sides of EADF, AE = 22, BE = 6, CF = 16 and BF = 2. Find the length of the line joining the mid-point of the sides AB and BC.

1. $4\sqrt{2}$
2. 5
3. 3.5
4. None of these

Q. Four horses are tied on the four corners of a square field of 14 m length so that each horse can just touch the other two horses. They were able to graze in the area 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. In the quadrilateral ABCD, AC = 7 cm, BD = 8 cm and $\angle AXD={60}^{\circ }$. Find the area of ABCD.

1. $28\sqrt{3}c{m}^2$
2. $14c{m}^2$
3. $28c{m}^2$
4. $14\sqrt{3}c{m}^2$