To find the height of an equilateral triangle, we can use the Pythagorean theorem.
In an equilateral triangle, the height splits the triangle into two right-angled triangles. Each of these right triangles has:
- A hypotenuse equal to the side length of the triangle (6 cm).
- One leg that is half of the base (which is 3 cm, since the base is the side length divided by 2).
- The other leg is the height we are trying to find.
Using the Pythagorean theorem, we can denote the height as h. The equation becomes:
h² + 3² = 6²
Now, simplifying this:
- h² + 9 = 36
- h² = 36 – 9
- h² = 27
- h = √27
- h = 3√3
Calculating the approximate value, we find:
- h ≈ 5.2 cm
Thus, the height of the equilateral triangle with a side length of 6 cm is approximately 5.2 cm.