Polygons(n>3)

Q. The height of the hexagon whose side is a

1. None of these
2. $\frac{3\sqrt{3}}{2}a$
3. $\frac{3\sqrt{3}}{4}a$
4. $\sqrt{3}a$

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 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. 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. If ABC is a quarter circle and a circle is inscribed in it and if AB = 1 cm, find the radius of the smaller circle.

1. $\sqrt{2}-1$
2. $\sqrt{2}+1)/2$
3. $\sqrt{2}-1/2$
4. $1-2\sqrt{2}$

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. 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. 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. 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 a parallelogram ABCD, the bisector of $\angle ABC$ intersects AD at E. If ED = 5, BE = 6, CE = 6, find AB?

1. 8
2. 4
3. 9
4. 6