# 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.

2
by Mittutti

2015-10-02T11:36:53+05:30

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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
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2015-10-02T11:45:36+05:30

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Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
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.