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?

Romanian school of geometry says:

ÄABC=ÄADE (BC=AE;<BAC=<ADE)=>AB=AD=1+AC=1+DE*=>AC=DE

*BD²=BC²+CD²=AE²+BH²(DH=perpendicular to the BA)

AD²=25+DE²=(1+DE)²=>2DE=25-1=>DE=12 =>Aria=2*(DE*AE)/2=60 inch

As Pythagoras once said: q.e.d. 

Posted by vije on 2004-07-10 10:50:30