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Problem of the Week
Problem D
A New Pi Plate

A pi-plate is in the shape of a regular hexagon with side length \(8\), and has an interesting pattern on it. From each vertex in the hexagon, a circular arc with centre at the vertex and radius \(8\) is drawn. This results in a flower-like pattern inside the hexagon, which is then shaded. Determine the total area of the shaded region.

The flower-like pattern consists of 6 identical petals.  Each petal extends from the centre of the hexagon to one of the 6 vertices. The 6 petals are shaded.