State whether the following statement is True or False and justify your answer:
The area of a regular hexagon of side $a$ is the sum of the areas of the five equilateral triangles with side $a$.
The area of a regular hexagon of side $a$ is the sum of the areas of the five equilateral triangles with side $a$.
(FALSE) The statement is False.
A regular hexagon can be divided into six equilateral triangles by joining its center to each of its vertices.
Since each of these six triangles is an equilateral triangle with side $a$, the total area of the regular hexagon is equal to the sum of the areas of these six equilateral triangles.
Therefore, the area of a regular hexagon of side $a$ is $6 \times (\text{Area of an equilateral triangle of side } a)$, not the sum of the areas of five such triangles.
A regular hexagon can be divided into six equilateral triangles by joining its center to each of its vertices.
Since each of these six triangles is an equilateral triangle with side $a$, the total area of the regular hexagon is equal to the sum of the areas of these six equilateral triangles.
Therefore, the area of a regular hexagon of side $a$ is $6 \times (\text{Area of an equilateral triangle of side } a)$, not the sum of the areas of five such triangles.
Explore More
Similar Questions
$A$ plot,in the shape of a quadrilateral $XYZW$,has $XY = 25 \, m$,$YZ = 60 \, m$,$ZW = 33 \, m$,$WX = 34 \, m$,and $XZ = 65 \, m$. Find its area. (in $, m^2$)
Medium
View SolutionThe diagonals of a rhombus are $16\,cm$ and $30\,cm$. Find its perimeter. (in $,cm$)
Medium
View SolutionThe diagonals of a rhombus are $40 \, cm$ and $42 \, cm$. Find its area in $cm^2$.
Medium
View Solution$A$ rectangular plot is given for constructing a house, having a measurement of $40 \, m$ long and $15 \, m$ in the front. According to the laws, a minimum of $3 \, m$ wide space should be left in the front and back each, and $2 \, m$ wide space on each of the other sides. Find the largest area where the house can be constructed (in $m^2$).
Medium
View SolutionArea of a square $= (........... )^{2}.$
Easy
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo