Q:

Find the area of a regular hexagon ABCDE with the given consecutive vertices A(-4,2) and B (0,5).A.30 units B.35 unitsC.65.0 units D.69.8 units

Accepted Solution

A:
Answer:Option C. [tex]65.0\ units^{2}[/tex]Step-by-step explanation:we know thatThe area of a regular hexagon can be divided into six equilateral trianglesApplying the law of sinesThe area is equal to[tex]A=6[\frac{1}{2}b^{2} sin(60\°)][/tex]whereb 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]