# The area of a regular hexagon of side ‘a’ is the sum of the areas of the five equilateral triangles with side a. Is the given statement true or false and justify your answer.

**Solution:**

Given, side of regular hexagon = a

Area of regular hexagon = sum of areas of five equilateral triangles with side a.

We have to determine if the given statement is true or false.

A regular __hexagon__ has 6 identical sides

On joining all the vertex at the centre, we will get 6 identical triangles

So, area of regular hexagon = sum of areas of 6 equilateral triangles

Therefore, the given statement is false.

**✦ Try This: **Find the area of a regular hexagon with each side 4 cm, if the area of an equilateral triangle is 4√3 cm² with side 4 cm.

Given, area of equilateral triangle = 4√3 cm²

We know that,

Area of regular hexagon = 6 × area of equilateral triangles

= 6 × 4√3

= 24√3 cm²

Therefore, the area of regular hexagon is 24√3 cm²

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 12

**NCERT Exemplar Class 9 Maths Exercise 12.2 Problem 7**

## The area of a regular hexagon of side ‘a’ is the sum of the areas of the five equilateral triangles with side a. Is the given statement true or false and justify your answer.

**Summary:**

The given statement “The area of a regular hexagon of side ‘a’ is the sum of the areas of the five equilateral triangles with side a” is false

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