In Fig. 32, `A B C D` is a rectangle of length `A B=40\ c m` and breadth `B C=25\ c mdot` If `P , Q , R , S` be the mid-points of the sides `A B ,\ B C ,\ C D\ ` and`\ D A` respectively, find the area of the shaded region.

A B C D is a rhombus and P ,\ Q ,\ R ,\ S are the mid-points of A B ,\ B C ,\ C D ,\ D A respectively. Prove that P Q R S is a rectangle.

D ,\ E ,\ F are the mid-points of the sides B C ,\ C A and A B respectively of a A B C . Determine the ratio of the areas of D E F and A B C .

In Figure, A B C D is a rectangle with sides A B=10 c m\ a n d\ A D=5c mdot Find the area of E F G

A B C D is a rectangle formed by joining the points A(-1,\ -1),\ \ B(-1,\ 4),\ \ C(5,\ 4) and D(5,\ -1)dot P ,\ Q ,\ R and S are the mid-points of sides A B ,\ B C ,\ C D and D A respectively. Is the quadrilateral P Q R S a square? a rectangle? or a rhombus? Justify your answer.

In Figure, triangle A B C is right-angled at Bdot Give that A B=9C M ,\ A C=15 C M ,\ a n d\ D ,\ E\ are the mid-points of the sides A B\ a n d\ A C respectively, calculate The length of B C (ii) The area of A D E

In Fig. 15.93, A B C D is a rectangle with A B=14\ c m and B C=7\ c m . Taking D C ,\ B C and A D as diameters, three semi-circles are drawn as shown in the figure. Find the area of the shaded region. (FIGURE)

If A B C D is a rectangle with /_B A C=32^0, find the measure of /_D B C

In Fig. 15.82, A B C D is a rectangle, having A B=20\ c m and B C=14\ c m . Two sectors of 180o have been cut off. Calculate: (i) the area of the shaded region. (FIGURE) (ii) the length of the boundary of the shaded region.

In Fig. 15.63, A B C D is a trapezium with A B D C and /_B C D=60o . If B F E C is a sector of a circle with centre C and A B=B C=7\ c m and D E=4\ c m , then find the area of the shaded region (U s e\ \ pi=(22)/7\ a n d\ sqrt(3)=1. 732) .

A B C D is a kite having A B=A D and B C=C D . Prove that the figure formed by joining the mid-points of the sides, in order, is a rectangle.