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Problem 76

Geometry Difficulty 1.1 Multiple choice CEMC Pascal · Canada · 2016

In the diagram, each of the five squares is $1 \times 1$ .

What percentage of the total area of the five squares is shaded?

Pick one

Official solution

Since the grid is made up of $1 \times 1$ squares, then the lengths of the solid line segments, from top to bottom, are 5, 1, 4, 2, 3, and 3.

The sum of these lengths is $5+1+4+2+3+3=18$ .

Alternatively, we could note that the first and second solid line segments can be combined to form a solid segment of length 6. The same is true with the third and fourth segments, and with the fifth and sixth segments. Thus, the total length is $6 \times 3 = 18$ .

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