Comparative Area of Regular Hexagon and Square

Consider a regular hexagon inscribed in a circle with a radius of 10 cm. Each vertex of the hexagon touches the circle. To calculate the area of the hexagon, we can use the formula:

$$ ext{Area} =\frac{3 oot{3} s^2}{2}$$

where $s$ is the length of each side. First, we need to find the length of a side of the hexagon. The formula for the side length $s$ of a regular hexagon inscribed in a circle is given by:

$$s = r imes oot{3}$$

where $r$ is the radius of the circumscribed circle. Calculate the area of the regular hexagon and determine the relationship between the area of the hexagon and the area of a square that has the same perimeter as the hexagon.