What is the altitude of an equilateral triangle with a side of 12 cm?*6 cm6√3 cm12√3 cm9 cm

1. Break Down the Problem

To find the altitude (height) of an equilateral triangle with a side length of $s = 12 \, \text{cm}$, we can use the formula for the altitude of an equilateral triangle:

$h = \frac{\sqrt{3}}{2} s$

2. Relevant Concepts

In an equilateral triangle, all sides are of equal length, and the altitude can be derived from the properties of 30-60-90 triangles. An altitude splits the triangle into two 30-60-90 triangles.

3. Analysis and Detail

Substituting the side length into the formula:

$h = \frac{\sqrt{3}}{2} \times 12$

Calculating this step-by-step:

1. Multiply $\sqrt{3}$ by 12: $\sqrt{3} \times 12 = 12\sqrt{3}$

2. Now divide by 2: $h = \frac{12\sqrt{3}}{2} = 6\sqrt{3} \, \text{cm}$

4. Verify and Summarize

The calculation results in an altitude of $6\sqrt{3} \, \text{cm}$. This can be verified by ensuring that the formula used is applicable for an equilateral triangle and that the calculations follow correctly.

Final Answer

The altitude of the equilateral triangle with a side length of 12 cm is $6\sqrt{3} \, \text{cm}$.