Question

How many convex pentagons are there in the figure given below?

• A. $10$
• B. $12$
• C. $8$
• D. $4$

Answer 1

The correct option is B $12$


A convex pentagon is a polygon with all interior angles smaller than ${180}^{\circ }$ and five sides.

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.