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  • Write 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.

Write 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.

Answers (1)

Solution

According to question

Area\; of\; regular\; hexagon = sum\; of\; area \; of\; five\; equilateral \; triangles

We know that a regular hexagon is divided into 6 equilateral triangles by its diagonals.

Area\; of\; 1\; equilateral\; triangle = \frac{\sqrt{3}}{4} \times a^{2}

Area\; of\; 6\; equilateral\; triangle =6\times \frac{\sqrt{3}}{4} \times a^{2}=\frac{3\sqrt{3}}{2}a^{2}

Area\; of\; 5\; equilateral\; triangle =5\times \frac{\sqrt{3}}{4} \times a^{2}=\frac{5\sqrt{3}}{4}a^{2}

Therefore the given statement is false.

Posted by

infoexpert21

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