The count of the equilateral triangle is an illustration of areas
There are 150 small equilateral triangles in the regular hexagon
The side length of the hexagon is given as:
L = 5
The area of the hexagon is calculated as:
[tex]A = \frac{3\sqrt 3}{2}L^2[/tex]
This gives
[tex]A = \frac{3\sqrt 3}{2}* 5^2[/tex]
[tex]A = \frac{75\sqrt 3}{2}[/tex]
The side length of the equilateral triangle is
l = 1
The area of the triangle is calculated as:
[tex]a = \frac{\sqrt 3}{4}l^2[/tex]
So, we have:
[tex]a = \frac{\sqrt 3}{4}*1^2[/tex]
[tex]a = \frac{\sqrt 3}{4}[/tex]
The number of equilateral triangles in the regular hexagon is then calculated as:
[tex]n = \frac Aa[/tex]
This gives
[tex]n = \frac{75\sqrt 3}{2} \div \frac{\sqrt 3}4[/tex]
So, we have:
[tex]n = \frac{75}{2} \div \frac{1}4[/tex]
Rewrite as:
[tex]n = \frac{75}{2} *\frac{4}1[/tex]
[tex]n = 150[/tex]
Hence, there are 150 small equilateral triangles in the regular hexagon
Read more about areas at:
https://brainly.com/question/24487155
