Question

A square and a regular hexagon have the same perimeter. If the area of the square is $2.25$, calculate the area of the hexagon.

• A. $2.250$
• B. $2.598$
• C. $2.838$
• D. $3.464$
• E. $3.375$

Answer 1

The correct option is B $2.598$

Let the side of square and perimeter is $a$ and $b$.

Now area of square is $2.25$

Area of square is $a^2$, where $a$ is side of square

$\Rightarrow a^2=2.25\Rightarrow a=1.5$

Perimeter of square and hexagon is $4a$ and $6b$ respectively and both are equal.

So, $4a=6b$

$\Rightarrow b=\frac{4a}{6}=\frac{3a}{2}=2.25$

Now area of hexagon is $\frac{3\sqrt{3}}{2}{a}^2$

$\Rightarrow \frac{3\sqrt{3}}{2}\times {2.25}^2\Rightarrow 2.598$