Calculate the area of the quadrilateral `A B C D` as shown in Fig.33, given that `B D=42\ c m` , `A C=28\ c m` , `O D=12\ c m` and `A C_|_B D` .

Calculate the area of quadrilateral field A B C D as shown in Fig.35, by dividing it into a rectangle and a triangle.

In a quadrilateral A B C D , given that /_A+/_D=90o . Prove that A C^2+B D^2=A D^2+B C^2 .

Find the area of the quadrilateral A B C D given in Figure. The diagonals A C and B D measure 48 m and 32 m respectively and are perpendicular to each other.

The perimeter of the sector O A B shown in Fig. 15.106, is (a) (64)/3c m (b) 26\ c m (c) (64)/5c m (d) 19\ c m (FIGURE)

In quadrilateral A B C D show in Figure. A B D C a n d A D_|_A Bdot Also, A B=8m , D C=B C=5mdot Find the area of the quadrilateral.

In a A B C , D a n d E are points on the sides A B and A C respectively. For each of the following cases show that D E B C : A B=12 c m , A D=8 c m , A E=12 c m a n d A C=18 c m . (ii) A B=5. 6 c m , A D=1. 4 c m , A C=7. 2 c m a n d A E=1. 8 cm

In Fig. 10.57, a circle is inscribed in a quadrilateral A B C D in which /_B=90o . If A D=23 c m , A B=29 c m and D S=5c m , find the radius r of the circle. (FIGURE)

In a A B C , D and E are points on the sides A B and A C respectively such that D E B C If A D=6\ c m , D B=9\ c m and A E=8\ c m , find A C . (ii) If (A D)/(D B)=3/4 and A C=15\ c m , find A E . (iii) If (A D)/(D B)=2/3 and A C=18\ c m , find A E .

In Fig. 4.60, check whether A D is the bisector of /_A of A B C in each of the following: (FIGURE) A B=5c m , A C=10 c m , B D=1. 5 c m and C D=3. 5 c m (ii) A B=4c m , A C=6c m , B D=1. 6 c m and C D=2. 4 c m (iii) A B=8c m , A C=24 c m , B D=6c m and B C=24 c m

A plot is in the form of a rectangle A B C D having semi-circle on B C as shown in Fig. 15.64. If A B=60\ m and B C=28\ m , find the area of the plot. (FIGURE)