Answer:
41.57 unit²
Step-by-step explanation:
We know,
Area of a regular hexagon = .
The length of the apothem = units.
<em>Since, we know, 'a regular hexagon splits into 6 identical equilateral triangles'.</em>
As, the apothem of the regular hexagon = height of the equilateral triangle
So, height of the equilateral triangle = units.
As, in the equilateral triangle, 'One of the side length is the S, other will be and height is units'.
So, using Pythagoras Theorem, we have,
i.e.
i.e.
i.e.
i.e.
i.e. [tex3S^2=48[/tex]
i.e. [texS^2=16[/tex]
i.e. S= 4 units
That is, the side length of the hexagon = 4 units.
Thus, the area of the hexagon is given by,
Area of a regular hexagon =
i.e. Area of a regular hexagon =
i.e. Area of a regular hexagon =
i.e. Area of a regular hexagon = 41.57 unit²
Hence, the area of the regular hexagon is 41.57 unit².