Question

In the adjoining figure ABCD is a trapezium in which parallel sides are AB 78 cm,DC 52 cm , and the non parallel sides are BC 30 cm,and AD 28 cm find the area of the trapezium

Answer 1

Answer:

Let us construct =DE ∣∣ CB

∴DC=EB=52 cm

DE=CB=30 cm

AE=AB−EB

=78−52=26 cm

For ΔADE,s=

28+30+26/2

=42

ΔDAE is a scalene triangle

Area(ΔDAE)=

s(s−a)(s−b)(s−c)

=

42(42−30)(42−28)(42−26)

=

42×12×14×16

=

6×7×6×2×7×2×4×4

=

6×6×7×7×2×2×4×4

=6×7×2×4

=336 cm

2

But we know Area(ΔDAE)=

1/2 ×AE×Height

⇒336= 1/2 ×26×h

= 336 = 13h

H = 336/13 cm

Area of trapezium ABCD=

1/2 ×h×(sum of parallel sides)

= 1/2 ×336/13 ×130

=1680 cm

Answer : 1680cm.sq