Respuesta :
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.
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.
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
Read more about areas at:
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