Question

The adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram.

Answer 1

let abcd is a parallelogram
ad=34
dc=20
and ac=42
in Δadc
s=34+20+42=48
area of adc=whole in under root(48*14*28*6)
area of adc=336 cm²
now, it is a parallelogram so,
ad=bc=34
dc=ab=20
ac common=42
so area of cba=336 cm²
adding adc and cba=336+336=672cm²
hene area of abcd=672cm²

Answer 2

ab=bc=34
dc=20 
ac=42
using herons formula  AREA of ΔACD 
√s(s-a)(s-b)(s-c)
√48(48-34)(48-20)(48-42)
√48*14*28*6
=336
AREA of Δabc=336
∵are of parellepgram abcd =336*2=672