The answer is 374.4 yards.
There are 2 ways to calculate the area of a <span>a regular hexagon.
It is given:
apothem: b = 10.4 yards
side: a = 12 yards
1. The direct way is to use the formula for the regular hexagon without using an apothem:
</span>
<span>where
A - the area of the </span><span>hexagon
a - the side of the </span><span>hexagon
Therefore:
</span><span>
</span><span>
</span><span>
</span>
2. The indirect way is to sketch the hexagon with 3 diagonals and create 6 triangles. Then, it is necessary to calculate the area of one triangle and multiply it by 6. In this triangle, apothem is actually the height.
The area of the hexagon is:
A = 6 · A₁
where:
A - the area of the <span>hexagon,
</span>A₁ - the area of the triangle
where
h - <span>height of the triangle.
</span>
Since apothem (b) of the hexagon is the height (h) of the triangle, then:
<span>
</span><span>
</span>
Thus, the area of one triangle is 62.4 yards.
To calculate the area of the hexagon, we will multiply it by 6:
<span>A = 6 · A₁
</span><span>A = 6 · 62.4
</span>A = 374.4 yards
<span>In both cases, the result is 374.4 yards.</span>The answer is
