A Parallelogram has sides 6cm and 4cm and one of its diagonals is 8cm long. Find the area.
Hello,
To understand and solve this question, first draw the parallelogram with its diagonal on a piece of paper. You will see that the parallelogram is divided into two triangles of equal area.
Now Multiply are of one triangle by 2,
We will get,
√ [s (s-a) (s-b) (s-c) ] x 2
where s = ( 6 + 4 + 8 ) divided by 2
s = 18/2
s = 9 cm.
by substituting the value of s in formula √ [s (s-a) (s-b) (s-c) ] x 2
we will get,
√ [9 (9-6) (9-4) (9-8) ] x 2
√[9 x 3 x 5 x 1] x 2
√135 x 2
6√ 15 or 23.2379 cm
So, the area of parallelogram is 6√ 15 or 23.2379 cm
Hope this was helpful.
Hello,
A diagonal divides parallelogram into two equal parts
so area = 2* (area of triangle with sides 6cm , 4cm , 8cm)
Let the area of the Triangle be A1
then area of parallelogram is 2*A1
for traingle of Area A1,
s=(6+4+8)/2=9
Then area of Traingle A1=sqrt(s(s-a)(s-b)(s-c)
A1=sqrt(9(9-6)(9-4)(9-8))
=sqrt(9*3*5*1)
=3*sqrt(15)
=3*3.87
=11.61
Therefore the area of parallelogram is 2*A1=2*11.61=23.23
Therefore area of the parallelogram is 23.23cm2
