You have 8 sticks. Three of them can form the sides of a right triangle with area 50.

But you can use all eight to form a cyclic (inscribable within a circle) octagon all of whose angles are equal. What would be the area of such an octagon?

A 10 x 10 square has an area of 100 but divided diagonally the right triangles so formed each have an area of 50; the three sticks that would bound one of these have lengths of 10, 10 and √200.

Laying 5 squares in the form of a Maltese cross (area 500) and inserting 4 right triangles of the dimensions noted above (area 200) forms an octagon whose vertices are cyclic. 

The total area is 700 square units.

Posted by brianjn on 2009-04-13 21:30:03