If follows that

**area of ABDE + area of BCFG = area of ACKL**.

Click here to see the GSP sketch. Verify that the above statement holds by dragging on the sketch.

**Prove that the area of ACKL is equal to the sum of the areas of ABDE and
BCFG.**

**PROOF:**

Extend LA to intersect ED in I and extend KC to intersect GF in L. Extend HB to intersect AC in M and to intersect LK in N. Since HB is parallel to LA and KC, we now know IL, HN, and LC are parallel.

Then **area of ABHI = area of ABDE** since AB is the base of each and they
have equal heights. Also **area BCFG = area of BCLH** since BC is the base
of each and they have equal heights. Click here to see a visualization that
these areas are equal.

Now AL = MN = CK = HB. So** area of ALNM = area of ABHI** since their
bases NM and HB are equal and they have equal heights. Therefore, **area of
ABDE = area of ALNM**.

Also **area MNKC = area of BCLH** since they have equal bases of HB and MN
and also have equal heights. Thus,** area BCFG = area of MNKC**.

It then follows that

** area ACKL = area of ALNM + area of MNKC = area of ABHI + area of
ACLH.**