Answer:
270[tex]\sqrt{3}[/tex] cm³
Step-by-step explanation:
A regular hexagon can be cut into 6 equilateral triangles.
The area (A) of an equilateral triangle can be calculated as
A = [tex]\frac{s^2\sqrt{3} }{4}[/tex] ← where s is the side length, here s = 6
A = [tex]\frac{6^2\sqrt{3} }{4}[/tex] = 9[tex]\sqrt{3}[/tex] cm² ← multiply by 6
area of base = 6 × 9[tex]\sqrt{3}[/tex] = 54[tex]\sqrt{3}[/tex] cm²
The volume (V) of the prism is calculated as
V = area of base × height = 54[tex]\sqrt{3}[/tex] × 5 = 270[tex]\sqrt{3}[/tex] cm³
