Question

A parallelogram has sides 34 cm and 20 cm. One of
its diagonals is 42 cm. Calculate its area.​

Answer 1

Answer:

Consider that on either side of the diagonal we have a triangle

with side lengths 34 , 20 , and 42.

So if we can find the total area of the two triangles we will have

the area of the parallelogram.

We can use Heron's formula to find the area of one of the triangles.

First we find s ( 1/2 the perimeter )

s = (1/2)*(34 + 20 + 42)

s = (1/2)*(96)

s = 48

The formula for the area A is A = sq-rt(s*(s-a)(s-b)(s-c))

so A = sq-rt( 48 * (48-34) * (48-20) * (48-42) )

A = sq-rt( 48 * 14 * 28 * 6 )

A = sq-rt( 112896 )

A = 336

The area of the parallelogram is twice 336 or 672.

So the answer is 672sq.cm