ABCD is a parallelogram with a base of BC. BFE is an straight line cut through the AD in equal 2 part at point F. CDE is another extendedstraight...

We have a parallelogram ABCD, with the point F dividing AD
in two equal parts.

Let us take the distance between the
sides BC and AD as d.

Now, BC*d = AD*d = 80
cm^2.

We have AF = AD/2

The
area of the triangle ABF is (1/2)*(AD/2)*d

= 80/4 = 20
cm^2

Similarly if we take the triangle DFC, the area is
(1/2)*(AD/2)*h

= 80/4 = 20
cm^2

The area of the triangle BFC is 80 - 20 - 20 = 40
cm^2.

Now we draw a line EX perpendicular to BC from the
point E.

If we consider angle
ECX,

sin ECX  =  EX / EC = d /
DC

we have DC = (EC /2)

So we
get EX = EC*d/DC

=>
EC*d*/(EC/2)

=> d*
2

The area of triangle BCE =
(1/2)*(BC)*EX

=>
(1/2)*BC*d*2

=>
BC*d

=> 80 cm^2

The
area of the triangle EFC = area of triangle BCE - area of triangle
BFC.

We have derived the area of the triangle BFC as 40, so
the area of EFC = 80 - 40 = 40
cm^2,

Therefore the area of the triangle BCE
is 80 cm^2, of triangle ABF is 20 cm^2 and of triangle EFC is 40
cm^2