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Problem 166

Geometry Difficulty 1.4 Multiple choice CEMC Gauss (Grade 7) · Canada · 2014

The diagonals have been drawn in the square shown.

The area of the shaded region of the square is

Pick one

Official 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 $^2$ .

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