Question

Two adjacent sides of a parallelogram are 34 cm and 20 cm. If one of its diagonal is 42 cm, find: area of the parallelogram.

Answer 1

At first we have to calculate the area of the triangle having sides 34cm, 20cm and 42cm.
Now,

s = ${\displaystyle \frac{34+20+42}{2}}$
= 48cm
∴ Area of triangle
= ${\displaystyle \sqrt{48(48-34)(48-20)(48-42)}}$
= ${\displaystyle \sqrt{48\times 14\times 28\times 6}}$
= ${\displaystyle \sqrt{4\times 12\times 2\times 7\times 4\times 7\times 2\times 3}}$
= ${\displaystyle \sqrt{4\times 4\times 2\times 2\times 7\times 7\times 36}}$
= 4 x 2 x 7 x 6
= 336cm² 
∴ Area of parallelogram
= 2 x Area of triangle
= 2 x 336
= 672cm².