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 = `(34 + 20 + 42)/(2)`
= 48cm
∴ Area of triangle
= `sqrt(48(48 - 34)(48 - 20)(48 - 42)`
= `sqrt(48 xx 14 xx 28 xx 6)`
= `sqrt(4 xx 12 xx 2 xx 7 xx 4 xx 7 xx 2 xx 3)`
= `sqrt(4 xx 4 xx 2 xx 2 xx 7 xx 7 xx 36)`
= 4 x 2 x 7 x 6
= 336cm² 
∴ Area of parallelogram
= 2 x Area of triangle
= 2 x 336
= 672cm².