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

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.

MrRoyal MrRoyal · Answer 2 · 2022-01-21T17:56:55+01:00

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

[tex]\cos(\theta/2) = \frac{a}{4}[/tex]

Make (a) the subject

[tex]a = 4\cos(\theta/2) [/tex]

The measure of theta is calculated using:

[tex]\theta = \frac{360}{n}[/tex]

So, we have:

[tex]\theta = \frac{360}{6} = 60[/tex]

The equation becomes

[tex]a = 4\cos(60/2) [/tex]

[tex]a = 4\cos(30) [/tex]

[tex]a = 3.46[/tex]

The area of the hexagon is then calculated as:

[tex]A = \frac 12 \times a \times n \times r[/tex]

This gives

[tex]A = \frac 12 \times 3.46 \times 6 \times 4[/tex]

[tex]A = 41.52[/tex]

Approximate

[tex]A = 42[/tex]

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