Mathematics
Problem of The Day
2024
95

95

The diagram shows six identical squares arranged symmetrically. What fraction of the diagram is shaded?

Source: UK JMO - 2017 - A6

Answer

11/24

SOLUTIOn

There are several ways to solve this problem. This solution is just one example.

Without loss of generality, let each square have a side length of 2 units. Hence the six identical squares have a total area of 6 x 22 = 24 square units. The grey shaded area can be thought of as consisting of two triangles, one rectangle and one square, as shown on the diagram.

Therefore the grey shaded area is 1/2 × 1 × 4 +1/2 × 3 × 2 + 1 × 2 + 22 = 11 square units.

Hence 11/24 of the diagram is shaded.

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