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Given:
Perimeter of equilateral triangle = 36 cm

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Formula:
Perimeter of an equilateral triangle = 3 * side length

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Finding the side length:
- Perimeter = 3 * side length
- 36 = 3 * side length
- side length = 36 / 3
- side length = 12 cm

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Finding the height:
- In an equilateral triangle, the height can be found by drawing a perpendicular line from one of the vertices to the base, splitting the base into two equal parts.
- This line divides the equilateral triangle into two 30-60-90 right-angled triangles.
- The height of the equilateral triangle is then calculated using trigonometry.
- In a 30-60-90 triangle, the height is √3/2 times the length of the side.
- Therefore, height = √3/2 * side length
- Substituting the values, height = √3/2 * 12
- height ≈ 10.39 cm

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Conclusion:
The height of the equilateral triangle with a perimeter of 36 cm is approximately 10.39 cm.