Answer:
259.8 cm²
Step-by-step explanation:
A regular hexagon can be cut into 6 equilateral triangles and an equilateral triangle can be divided into two 30°- 60°- 90° triangles
Note that the apothem (5[tex]\sqrt{3}[/tex]) divides the triangle into two equilateral triangles, thus
The apothem is the long leg (the x[tex]\sqrt{3}[/tex]) side of a 30- 60- 90 triangle, so
x[tex]\sqrt{3}[/tex] = 5[tex]\sqrt{3}[/tex] ⇒ x = 5
Thus the side length of the hexagon = 2 × 5 = 10
and the perimeter = 6 × 10 = 60
A = [tex]\frac{1}{2}[/tex] × perimeter × apothem
= 0.5 × 60 × 5[tex]\sqrt{3}[/tex] = 150[tex]\sqrt{3}[/tex] ≈ 259.8 cm²
