Question

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Answer 1

The count of the equilateral triangle is an illustration of areas

There are 150 small equilateral triangles in the regular hexagon

How to determine the number of equilateral triangle

The side length of the hexagon is given as:

L = 5

The area of the hexagon is calculated as:

$A = \frac{3\sqrt 3}{2}L^2$

This gives

$A = \frac{3\sqrt 3}{2}* 5^2$

$A = \frac{75\sqrt 3}{2}$

The side length of the equilateral triangle is

l = 1

The area of the triangle is calculated as:

$a = \frac{\sqrt 3}{4}l^2$

So, we have:

$a = \frac{\sqrt 3}{4}*1^2$

$a = \frac{\sqrt 3}{4}$

The number of equilateral triangles in the regular hexagon is then calculated as:

$n = \frac Aa$

This gives

$n = \frac{75\sqrt 3}{2} \div \frac{\sqrt 3}4$

So, we have:

$n = \frac{75}{2} \div \frac{1}4$

Rewrite as:

$n = \frac{75}{2} *\frac{4}1$

$n = 150$

Hence, there are 150 small equilateral triangles in the regular hexagon

Read more about areas at:

brainly.com/question/24487155