There is a pentagon ABCDE such that angles A, C, and E are all right angles and it is concave at angle C.

If a ray starting at D was aimed at C, it would go exactly 1 inch before going through C, and would eventually go through A.

If BC and AE are both 5 inches, what is the area of this pentagon?

OK, so angle C is 270 degrees.  Angles E and A are adjacent right angles, so AB and ED are parallel lines.  C is between those 2 lines and closer to the AE segment than either B or D.  And since BC is 5 and CD is 1, BD (which is not part of the pentagon) is sqrt(26).  ED is 1 inch shorter than AB.

Posted by Larry on 2004-06-12 11:58:56