Question

Find the area of the regular polygon with a side length of 48

Answer 1

Answer:

The area of the regular polygon i.e. regular hexagon with a side length of 48 is:

• $A\approx 5985.97$

Step-by-step explanation:I

• If all sides of a polygon are equal in length, then it will be a regular polygon.

For example, a regular hexagon is a regular polygon which has all six sides equal in length as show in attached figure below.

As one side of the length of a regular hexagon (regular polygon) = a = 48

We can determine the area using  the formula:

$A\:=\:\frac{3\sqrt{3}}{2}a^2\:$

Putting a = 48 in the formula to determine the area

$A\:=\:\frac{3\sqrt{3}}{2}\left(48\right)^2\:\:\:\:$

$\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}$

$A=\frac{3\sqrt{3}\cdot \:48^2}{2}$

$\mathrm{Factor}\:48^2:\quad 2^8\cdot \:3^2$

  $=\frac{2^8\cdot \:3^2\cdot \:3\sqrt{3}}{2}$

  $=\frac{2^8\cdot \:3^3\sqrt{3}}{2}$

$\mathrm{Cancel\:the\:common\:factor:}\:2$

$A=2^7\cdot \:3^3\sqrt{3}$

$A=3^3\cdot \:128\sqrt{3}$     ∵ $2^7=128$

$A=128\cdot \:27\sqrt{3}$

$A=3456\sqrt{3}$

$A\approx 5985.97$

Therefore, the area of the regular polygon i.e. regular hexagon with a side length of 48 is:

• $A\approx 5985.97$