Question

The adjacent sides of a parallelogram are 20 cm and 34 cm and one of its diagnols is 42cm.Find area of parallelogram

Answer 1

From the diagram, diagonal AC divides the parallelogram ABCD into two equal triangles.

So, area of parallelogram ABCD = 2 x area of ΔABC
       
To find the area of parallelogram, we have to find the area of ΔABC

AREA OF ΔABC:
we know that,

perimeter of triangle s = a+b+c/2  (where, a=34 cm, b=20 cm, c = 42 cm)
So, s = 34+20+42/2 = 96/2 = 48 cm.

Then area of ΔABC = √s(s-a)(s-b)(s-c) cm²
                                = √48(48-34)(48-20)(48-42) cm²
                                = √48 x 14 x 28 x 6 cm²
                                = 336 cm²

Then by using, area of parallelogram ABCD = 2 x area of ΔABC

Area of parallelogram ABCD = 2 x 336 cm² = 672 cm²

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Answer 2

Step-by-step explanation:

refer the attachment for clear understanding