Question

Qa au If the figure given below , AD = BC, LA -LC = 90°. ALSO AB - (2y +10) cm DC = (y + 20cm , LABD = x, LCDB=500, find nandy А 200 (24+10)cm D Jsou B (y+20)cm​

Answer 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

So, Area of trapezium:-

=

2

1

×(AB+CD)×height

=

2

1

×(75+30)×33.6=1764cm

2