Length of diagonals of parallelogram r 8 & 10 cm, angle included between diagonals is 60 degree. Find the area of parallelogram.

The area of parallelogram could be found in various ways. One formula says that area of parallelogram is the sum of the areas of the 4 triangles which are formed by diagonals, inside of parallelogram.

We name the diagonals: AC and BD. The intersection between them is the point O. We know that the 2 segments (AO=OC and BO=OD) which are the result of the intersection of diagonals are equal, so AO=OC=5cm and BO=OD=4cm.

The triangle formed is AOD, in which we know the following:

2 sides and the angle between:

AO=5cm, DO=4cm and <AOD=60

AREA OF AOD TRIANGLE= (AO*OD*sin60)/2=(5*4*0.86)/2=8.6cm^2

AREA OF AOB TRIANGLE = (AO*OB*sin 120)/2= (5*4* 0*86)/2=8.6cm^2

AREA OF PARALLELOGRAM ABCD= 4*8.6= 34.4cm^2