## Answer

"It's impossible to tell from the information you have given. An
unlimited number of shapes could have the dimensions given. We
would need to know one interior angle to calculate the area. It
would probably be necessary to know two in a strict mathematical
sense, but one would narrow it down to two possibilities, one of
which would be unlikely because it would be sort of a crescent
shape."

Although this is technically the right answer... . Using autocad
I drew a trapezoid. The two parallel sides are 50' and 30'. On the
left of the quadrilateral is the 64' side, and the side that is out
of square comes out to roughly 67'-11-1/16". This to me indicates
that your teacher attempted to indicate a trapezoid, with two right
angles, and that the measurement of the final side was an
approximation. This would keep you from being confused by feet,
inches, and fractions of inches, which are a pain. If indeed two
sides are parallel, the formula is H*((W1+W2)/2). What this means
is that the side which is "square", but that is not parallel to any
other line, is the height. In this case 64. W1 and W2 represent the
two parallel sides and are 50 and 30. Therefore, what you are doing
is taking an average width for the figure, and multiplying that by
the height, in order to determine the area. 64*((50+30)/2)= 64*40 =
2560. In order to calculate the area of an irregular figure, you
use a square to create right triangles. If no such dimensions
exist, you must use a scale to approximate the size of each
triangle in order to get the dimensions, and then use the formula
(H*W)/2 to calculate each triangle's area. You then add the area of
each triangle to get the total area. I assume your teacher's
drawing was actually a trapezoid.