5Question: A marine microbiologist studies a hexagonal coral colony with side length 3 cm. What is the area of the hexagon in square centimeters?
["Title: How to Calculate the Area of a Hexagonal Coral Colony – A Marine Microbiologist’s Insight (With Hexagon Side Length = 3 cm)", "Meta Description: Learn how marine microbiologists calculate the area of hexagonal coral colonies. This guide explains the formula, steps, and real-world application with a 3 cm hexagon side length.", "---", "### Understanding the Area of a Hexagonal Coral Colony", "Used by marine microbiologists studying coral reef ecosystems, determining the area of coral formations helps assess growth rates, biodiversity, and reef health. One common coral shape is a regular hexagon, with equal sides and equal interior angles. For a coral colony with a side length of 3 cm, understanding its geometric properties is essential.", "## What Is the Area of a Regular Hexagon?", "A regular hexagon can be divided into six equilateral triangles, each with sides equal to the hexagon’s side length. The formula for the area ( A ) of a regular hexagon with side length ( s ) is:", "[\nA = \frac{3\sqrt{3}}{2} s^2\n]", "This formula derives from the sum of the areas of these six equilateral triangles, each having area ( \frac{\sqrt{3}}{4} s^2 ).", "## Applying the Formula to a Coral Colony with Side Length 3 cm", "Let’s calculate the area when the hexagon’s side length ( s = 3 ) cm:", "[\nA = \frac{3\sqrt{3}}{2} \ imes (3)^2 = \frac{3\sqrt{3}}{2} \ imes 9 = \frac{27\sqrt{3}}{2} \ ext{ cm}^2\n]", "Approximate value:\n( \sqrt{3} \approx 1.732 )\n[\nA \approx \frac{27 \ imes 1.732}{2} = \frac{46.764}{2} = 23.382 , \ ext{cm}^2\n]", "## Why Is This Calculation Important?", "Marine microbiologists and ecologists use such measurements to:\n- Monitor coral colony growth over time\n- Compare structural health across reef zones\n- Model habitat spaces for marine microorganisms and invertebrates", "Knowing the precise area supports ecological research and keeps track of reef resilience in changing ocean conditions.", "## Summary", "Calculating the area of a hexagonal coral colony with a side length of 3 cm yields:", "[\n\boxed{ \frac{27\sqrt{3}}{2} \ ext{ cm}^2 \approx 23.38,\ ext{cm}^2 }\n]", "This geometric knowledge empowers scientists in uncovering the intricate balance of marine ecosystems—one hexagon at a time.", "---", "Keywords: marine microbiologist, hexagonal coral colony, coral area calculation, regular hexagon area formula, 3 cm hexagon, marine ecology, coral reef research, geometry in biology", "Bonus: Use this method to analyze coral growth, inform reef conservation strategies, and support climate change impact studies!", "---", "For updates on coral microbiology and reef science, follow reputable marine research journals and oceanographic institutions."]
