SOLUTION: a parallelogram has sides 34 cm and 20 cm .one of its diagonal is 42 cm.calculate its area

Question 814639: a parallelogram has sides 34 cm and 20 cm .one of its diagonal is 42 cm.calculate its area
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
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.
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