Question

a hexagon has a radius measuring 23 cm. what is the approximate area of the hexagon?
686.6 square cm
793.5 square cm
1374.4 square cm
1587.0 square cm

Explanation:

Step1: Find the side length of the hexagon

For a regular hexagon, the radius \(r\) is equal to the side length \(a\). So \(a = 23\) cm.

Step2: Use the formula for the area of a regular hexagon

The formula for the area \(A\) of a regular hexagon is \(A=\frac{3\sqrt{3}}{2}a^{2}\).
Substitute \(a = 23\) into the formula:

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Since \(\sqrt{3}\approx1.732\), then \(A=\frac{1587\times1.732}{2}\)

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Answer:

1374.4 square cm