Answer:
Option C. [tex]65.0\ units^{2}[/tex]
Step-by-step explanation:
we know that
The area of a regular hexagon can be divided into six equilateral triangles
Applying the law of sines
The area is equal to
[tex]A=6[\frac{1}{2}b^{2} sin(60\°)][/tex]
where
b is the length side of the regular hexagon
The length side of the regular hexagon is equal to the distance from consecutive vertices A(-4,2) and B (0,5)
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
substitute the values
[tex]b=\sqrt{(5-2)^{2}+(0+4)^{2}}[/tex]
[tex]b=\sqrt{(3)^{2}+(4)^{2}}[/tex]
[tex]b=\sqrt{25}[/tex]
[tex]b=5\ units[/tex]
Find the area
[tex]A=6[\frac{1}{2}(5)^{2} sin(60\°)]=65.0\ units^{2}[/tex]
