Areca is an incorrect name, the correct one being Dypsis lutescens.
I grew mine from seed about 10 years ago (don't ask me why, because it
is easier, quicker and cheaper to buy an established plant) and it's
just over 2.15m (7ft.) high. It sits in a corner of my sitting room
and gets indirect sunlight from a window opposite. This species does
not appreciate long periods of dryness and cannot grow properly unless
there is sufficient root moisture. That is not to say it must be kept
sopping wet, just that watering needs to be thorough whenever the
compost starts to dry out. Push your finger into the compost and if
it feels dry about 1cm down, then the plant needs a good watering.
This will be needed more often in summer than in winter, but there is
no rule that says you must water once a week etc.

The problem with giving those small dribbles of water is that you
increase the risk of salts building up within the compost and Dypsis
is rather sensitive this. Eventually the salt build-up becomes too
great and an otherwise healthy plant suddenly deteriorates. It
happens to a lot of house plants and after over or under-watering, is
one of the commonest causes of failure. The only solution is to
regularly wash out these salts by thorough drenching. Let the excess
water drain away completely before returning the plant to its normal
position. Never stand your palm in water, it will cause roots to rot
and increase stagnation within the compost.

Mine gets hauled into the shower, is treated to a 'torrential
rainstorm' and then allowed to drain overnight. As for feeding; I'm
lazy and push a few Miracle Grow slow-release pellets into the compost
every 6-8 months. Any good quality liquid feed applied every 2-3
weeks is fine, but make sure you use one that contains trace elements
as well as the main nutrients.

Now to your plant. If it has not been re-potted recently, now would
be a good time to look at that. Re-potting does not mean putting the
plant into a bigger pot, that's potting-on. It is all about making
sure that the compost is fresh and sustaining. Old, soil-less compost
will have lost all of its limited nutrients and be stale, acidic and
airless. It needs replacing with fresh if the plant is to flourish.
Carefully remove the plant from its pot and very gently tease out as
much of the old compost as you can without breaking or disturbing the
roots. Using good quality multi-purpose (or one with John Innes
added), reposition the plant in its old pot (having cleaned that
first) and shake in fresh compost. Agitating the pot while adding the
compost ensures that it trickles down around the roots and reduces the
risk of large air pockets. Water thoroughly and allow the plant to
drain.

Don't expect your plant to recover overnight. Even the fastest
growing palms are slow to show signs of recovery and tend to stop if
subjected to root disturbance, so it will take a few months before you
notice any appreciable improvement. It's a bit like a ship - takes a
long time to slow down and just as long to speed up. However, the
deterioration will subside unless your plant has gone too far and it
will be looking a lot healthier by late summer.