Question

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 units
C.65.0 units
D.69.8 units

Answer 1

Option C.
`65.0\ units^(2)`

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

`A=6[(1)/(2)b^(2) sin(60\°)]`

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

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

substitute the values

`b=\sqrt{(5-2)^(2)+(0+4)^(2)}`

`b=\sqrt{(3)^(2)+(4)^(2)}`

`b=√(25)`

`b=5\ units`

Find the area

`A=6[(1)/(2)(5)^(2) sin(60\°)]=65.0\ units^(2)`