Library / CEMC Gauss (Grade 8) /298 of 525

CEMC Gauss (Grade 8), 2014

Geometry Difficulty 1.4 Junior Find the answer Canada

If two straight lines intersect as shown, then $x - y$ is

Pick one

Solution

The two diagonals of a square bisect one another (divide each other into two equal lengths) at the centre of the square.

Therefore, the two diagonals divide the square into four identical triangles.

One of these four triangles is the shaded region which has area equal to one quarter of the area of the square.
Since the area of the square is $8\times 8=64$ cm $^2$ , the area of the shaded region is $64\div 4=16$ cm $^2$ .

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.