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

AC=42cm
AB=20cm
BC=34cm
USING HERONS FORMULA = √s(s-a)(s-b)(s-c) area of ΔABC
42+20+34/2=48
⇒√48(48- 42)(48-20)(48-34)
⇒√48*6*28*14
⇒336
∵area of ΔABC=336cm
now, area of parallelogram ABCD= 336*2=672cm

Answer 2

Area of the parallelogram=sum of the area of the two triangles, made by any one of the diagonal, right!!!
Area of a triangle=1/2*base*height
Here, we know all the three sides- 34,20,42.
So, we have to use the Heron's formula.

s=semi-perimeter=34+20+42/2
=96/2
=48 cm.
Let a=34, b=20; and, c=42.
Area of a triangle, =√s(s-a)(s-b)(s-c)
=√48(48- 34)(48-20)(48-42)     It is because s=48, a=34, b=20, c=42.
=√48*14*28*6
=√112896
=336 cm².

Therefore, are of the parallelogram= 2*336
=672 cm².

Thank you.
Hope this will help you.