Question

how many equilateral triangles of side 10m are there in the hexagonal plot​

Answer 1

Given,

The length of each side of the hexagon = 10 metres

To find,

The number of equilateral triangles that can be placed into that hexagon.

Solution,

We can easily solve this mathematical problem, by the following mathematical process.

We have keep in mind, the following geometrical property :

• The length of the diagonal of hexagon is double than the length of one side of the hexagon.
• The diagonals of the hexagon bisect each other or intersect at their common midpoint.

Now, there can be three primary diagonals of a hexagon, which geometrically divides the whole hexagon into 6 individual triangles.

Now, the one side of one of those triangles is the side of the hexagon itself. Other two sides are two half portions of two different diagonals.

Now, 2× side = diagonal

side = ½ × diagonal

So, the second and third sides of the triangle is also equal to the length of the one side of the hexagon itself.

The three sides of one of those three triangles are equal and this is applicable for all the 6 internal triangles.

Hence, the hexagon can be divided into 6 equilateral triangles.