Question

What is the area of a regular hexagon with a distance from its center to a vertex of 1 cm? (Hint: A regular hexagon can be divided into six equilateral triangles.)

Answer 1

Answer:

Exact area = $\frac{3}{2}\sqrt{3}$ square cm

Approximate area = 2.598 square cm

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Work Shown:

s = side length of equilateral triangle = 1 cm

A = area of equilateral triangle with side length 's'

$A = \frac{\sqrt{3}}{4}*s^2$

$A = \frac{\sqrt{3}}{4}*1^2$

$A = \frac{\sqrt{3}}{4}$

This is just one of the 6 equilateral triangles (see diagram below)

Multiply by 6 to get the area of all 6 equilateral triangles, or the entire hexagonal area

$6*A = 6*\frac{\sqrt{3}}{4}$

$6A = \frac{3\sqrt{3}}{2}$

$6A \approx 2.598$