ABCD is trapezium as shown in gure. Distance between two parallel sides AB
and CD is h. DC = 2AB = 2h. Area of ABCD = 384. F

1 thought on “ABCD is trapezium as shown in gure. Distance between two parallel sides AB<br /> and CD is h. DC = 2AB = 2h. Area of ABCD = 384. F”

1. Answer:

   Draw CE∥DA and CF⊥AB.

   Therefore, ADCE is a parallelogram having AE∥CD and CE∥DA.

   ⇒AD=CE=39cm,DC=AE=30cm and BE=75−30=45cm

   In △BCE, by heron’s formula we have

   a=39cm,b=45cm and c=42cm

   ⇒s=

   2

   a+b+c

   =

   2

   39+42+45

   =63cm

   ∴ Area of ΔBEC=

   s(s−a)(s−b)(s−c)

   =

   63(63−39)(63−42)(63−45)

   cm

   2

   =

   63×24×21×18

   cm

   2

   =756cm

   2

   Also, Area of ΔBEC=

   2

   1

   ×base×height

   ⇒

   2

   1

   ×45×h=756cm

   2

   ⇒h=33.6cm

   Reply