Question

There is a field in the shape of a trapezium ABCD. Two perpendiculars are dropped, BE from B to the base CD and AF from A to the base CD. EC : DC = 1 : 3, BE : EC = 1 : 1 and AB : BE = 3 : 2 and BC = 25 m. Find the area of the trapezium in m2. A) 720.3 B) 744.3 C) 680.3 D) 705.3​

Answer 1

Answer:

=1764cm

Step-by-step explanation:

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) cm2

=  63×24×21×18cm  2

=756cm  2

Also, Area of ΔBEC= 1/2×base×height

⇒ 21×45×h=756cm 2

⇒h=33.6cm

So, Area of trapezium:-  

= 1/2×(AB+CD)×height

= 1/2 ×(75+30)×33.6

=1764cm