Question

The regular hexagon has a radius of 4 in. What is the approximate area of the hexagon? 24 in.2 42 in.2 48 in.2 84 in.2

Answer 1

The central angle of a hexagon is 60°. Dividing it by two will give us 30°. The side opposite to 30° is 2 inches, multiplied by 2 is 4 inches. Thus, each side of the hexagon is 4 inches. Also, the apothem is 2sqrt(3). The area of the figure is calculated through the equation,
                                           A = 0.5aP
where a is apothem and P is perimeter
Substituting,
                                           A = 0.5(2sqrt3)(4 x 6) = 24sqrt3
The answer is approximately 41.57 in².

Answer 2

The approximate area of the hexagon is (b) 42

The radius of the hexagon is given as:

• Radius: r = 4

Start by calculating the length of the apothem (a) using the following cosine ratio

$\cos(\theta/2) = \frac{a}{4}$

Make (a) the subject

$a = 4\cos(\theta/2)$

The measure of theta is calculated using:

$\theta = \frac{360}{n}$

So, we have:

$\theta = \frac{360}{6} = 60$

The equation becomes

$a = 4\cos(60/2)$

$a = 4\cos(30)$

$a = 3.46$

The area of the hexagon is then calculated as:

$A = \frac 12 \times a \times n \times r$

This gives

$A = \frac 12 \times 3.46 \times 6 \times 4$

$A = 41.52$

Approximate

$A = 42$

Hence, the approximate area of the hexagon is (b) 42

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