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Count the number of convex pentagons in the adjoining figure.

Correct Answer: 12

Explanation:

A convex pentagon has no angles pointing inwards. More precisely, no internal angles can be more than 180°.

The figure may be labelled as shown.

The pentagons in the figure, are ABDFH, CDFHB, EFHBD, GHBDF, ACDFG, CEFHA, EGHBC, GABDE, BDEGH, DFGAB, FHACD and HBCEF. Clearly, these are 12 in number.

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