Q18. - Geometry

Question

Find the area of each figure:

A regular hexagon with perimeter 60 .

Step-by-Step Solution

Answer

The area of given figure is $150\sqrt{3}$ square units.

Step 1. Given information.

Perimeter of regular hexagon is60  .

Step 2. Analyze the given information.

Regular Hexagon has six equal sides. 

Let the side of hexagon be  

So, we can conclude 

 $a+a+a+a+a+a=60$

 $\Rightarrow 6a=60$

 $\Rightarrow a=10$

Step 3. Find the area of given figure.

Area of regular hexagon can be found using the formula 

$A=\frac{3\sqrt{3}}{2}{a}^2$ 

    $=\frac{3\sqrt{3}}{2}{\left(10\right)}^2$ 

  $=\frac{3\sqrt{3}}{2}\times 100$   

 $=150\sqrt{3}$    Square units.

Therefore, the area of given figure is $150\sqrt{3}$ square units.