Question

Find the area of the regular hexagon if its side is \[4\] \[cm\] .
(A) \[24\sqrt 3 \] \[c{m^2}\]
(B) \[4\sqrt 3 \] \[c{m^2}\]
(C) \[5\sqrt 3 \] \[c{m^2}\]
(D) \[2\sqrt 3 \] \[c{m^2}\]

Answer 1

Hint: A hexagon is a polygon with six sides . The word “hexa ” stands for six . In a regular hexagon all sides are of equal length and all angles are equal . We know the formula for the area of a regular hexagon. There we need to put the value of the length of one side and we will get the area of the hexagon .
FORMULA USED: Area of regular hexagon \[\dfrac{{3\sqrt 3 }}{2} \times {a^2}\] \[c{m^2}\] . Here \[a\] is the length of one side of the hexagon.

Complete answer:A regular hexagon has equal sides and equal angles . Here we know that the length of one side is \[4\] \[cm\]. So for this problem \[a\] is equal to \[4\] \[cm\] .
Now we have to find the area of the hexagon using the formula mentioned above .

Area of the hexagon is \[\dfrac{{3\sqrt 3 }}{2} \times {a^2}\] \[c{m^2}\]
Putting the value of \[a\] we get area of the hexagon = \[\dfrac{{3\sqrt 3 }}{2} \times {4^2}\] \[c{m^2}\]
We know square of four is sixteen so putting that value we get area of the hexagon =
 \[\dfrac{{3\sqrt 3 }}{2} \times 16\]\[c{m^2}\]
Sixteen can be divided by two . \[\dfrac{{16}}{2}\]= \[8\]
So after this calculation area of hexagon = \[3\sqrt 3 \times 8\]\[c{m^2}\]
Three times eight is twenty four . Applying this at last we get the area of the hexagon finally which is equal to \[24\sqrt 3 \] \[c{m^2}\].
So the correct answer to this problem is (A).

Note:
Unit of length is \[cm\] and unit of area is \[c{m^2}\] . Whenever we use the word area or formula of area then we have to use \[c{m^2}\] . In this problem we are dealing with regular hexagons . In a regular hexagon all sides are equal and all angles are also equal . Summation of all the interior angles of the hexagon is \[{720^0}\]. So each interior angle is \[{120^0}\]. Regular hexagon has \[9\] diagonals .