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Superbowl Helmet Puzzle

It's Superbowl LII day today. Superbowls, clock-faces, and occasionally fancy documents still use Roman Numerals (along with Kings, Queens, Popes and the Olympic Games).

Here's a quick geometry puzzle that you might like to knock-out during the half-time concert. It's not too challenging once you see the trick that makes it easy.

In the diagram below (which is supposed to look like a football helmet), an equilateral triangle with a side length of the diameter, is overlaid over the circle so that it passes through the centre of the circle. The question is to determine the area of the shaded region.

What is the area of the shaded region?


Have a quick think, then click the button below to reveal the solution.


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