Question

Area of the base of a hexagonal prism whose side is units. Find the area of the base?
$A)\dfrac{{\sqrt 3 }}{4}{a^2}$
$B)2 \times \dfrac{{\sqrt 3 }}{4}{a^2}$
$C)3\dfrac{{\sqrt 3 }}{2}{a^2}$
$D){a^2}$

Answer 1

Hint: First we have to define what the terms we need to solve the problem are. Since there were asking to find us the area of the base of the hexagon prism, first we need to know about the hexagon and the area of the base; hexagon means there are six sides of the slides or the shapes like a triangle, the square has three and four slides or shapes or lines joined respectively;
Area of the base means to find the equals parts divides the part of the slides or area;

Complete answer:

(Similarly in the backside of the hexagon contains three units a)
Let the sides of the given hexagons are sides are units. But all the options containing units. So, we need to simplify the given question further. Since the hexagon has six sides that means there are a total of six units of pairs of units.
The area can be calculated as the equals of six into the times of the area of the equilateral triangle, so divide the slides of the hexagon into the triangle; so that we are able to find the left side angle of the cube.
Hence $Area = 6 \times (\dfrac{{\sqrt 3 }}{4}){a^2}$(root three is the triangle left side cube and a is the unit also we need to multiply six times the resultant)
Thus, solving we get $Area = 6 \times (\dfrac{{\sqrt 3 }}{4}){a^2} \Rightarrow \dfrac{{3\sqrt 3 }}{2}{a^2}$Hence the option $C)3\dfrac{{\sqrt 3 }}{2}{a^2}$ is correct
Also, there is no possibility of getting the answer as $D){a^2}$because we already know in a triangle there are three sides; so the square root of the three will definitely be in the answer; and also left side area of the hexagon contains three to $A)\dfrac{{\sqrt 3 }}{4}{a^2}$,$B)2 \times \dfrac{{\sqrt 3 }}{4}{a^2}$thus option A and B eliminated too;

Therefore, the correct option is C

Note: \[Area = {\text{ }}6 \times (area{\text{ }}of{\text{ }}equilateral{\text{ }}triangle)\]of the left side cube which asked in the given question.
Since the unit of the hexogen, the base of the hexagonal prism is the hexagon with six sides, as solved above.
 L.S.A is the left side angle of the cube.