Question

find the area of a regular hexagon with side 2 sqrt 3 cm and apothem 3 cm.

Answer 1

The apothem of a regular polygon is a line segment from the center to the midpoint of one of its sides.

If you break the hexagon into six congruent triangles, each triangle will have a base of 2sqrt(3) and apothem, which is the perpendicular height, 3. The area of a triangle is \[1/2 \times (base) \times (perpendicular.height)\]which is \[\frac{1}{2} \times 2 \sqrt{3} \times 3= 3 \sqrt{3}\]But you have six of these triangles, so your area is then\[6 \times 3 \sqrt{3} = 18 \sqrt{3}\]