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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