If a trapezoid has a top base of 6 and a bottom base of 30 and a height of 15, what is its area?

For a REGULAR Trapezoid (sides EQUAL) ---> A or
B

>>> METHOD
A-

You need to think of the imaginary lines which come down
as the perpendicular from the TOP and hit perpendicular to the
bottom.

See them
yet?~@

Cutting along those lines, that leaves you with ONE
rectangle 6 by 15 [units] and two triangles with height 15 and *___
base.

One of those triangles could be cut loose from the
rectangle and rotated so that the hypotenuse [long side] joins to its twin. Now you
COULD do the area for two indentical triangles, BUT one rectangle is just as
easy.

NOW, add the areas together (6 x 15) + (15 x *___) =
Area of Trapezoid

** It is YOUR homework, so YOU figure out
what is left and take half that fill in the blank and get the whole
answer.

~@ If you have trouble visualizing it, make a
template out of graph paper, and cut your lines. Superimpose the trapezoid on the grap
paper grid; 6 top, 15 down, base 30
(centered)

>>>>
METHOD B-

MENTALLY, (or actually on a grid ) Cut the
trapzoid down the center on a perpendicular. Rotate and flip the pieces so that the
diagonal sides meet and you SHOULD be able to see an NEW Rectangle from the pieces, and
THEN find the area easiest.

++++ IRREGULAR
Trapezoid (Unknown/Uneven sides)

You need to take the AREA
of two triangles made from the figure cut on a diagonal from one corner to the opposite
corner {Trap- ABCD, diagonal from corners A-C}

See it in
your head yet?

NOW you should be on easy street AND better
understand why there IS a formula for the trapezoid area (which must be paraphrased by
this discussion limitations):

1/2(Btop)(H) +
1/2(Base)(H)

^^^^

OK,
so I explained how to MAKE the CLOCK instead of telling you what time it was! Give them
all a go, find your favorite explanation and USE it!

ONE
problem does not always have ONE solution.