Math CentralQuandaries & Queries


Question from Amit, a teacher:

A rectangular sheet of a paper with dimensions a and b is folded along its diagonal. What is the area of the overlapped region?


I folded the sheet of paper CDBP along the diagonal CB so that P moved to A. then drew a line segment EF to meet BC in a right angle at F. Let |CA| = a, |AB| = b and then |BC| = c where c2 = a2 + b2 by Pythagoras' Theorem.

folded sheet

By the symmetry F is the midpoint of BC. Let |EF| = h, the height of triangle CEB.

Triangles ABC and EBF are similar.

Can you complete the problem now?

About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS