From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14 cm, 10 cm and 6 cm. Find the area of the triangle.

Explanation

To find the area of the equilateral triangle given the lengths of the perpendiculars from a point inside the triangle to its sides, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- We have an equilateral triangle \( ABC \).
- The lengths of the perpendiculars from point \( P \) to the sides \( BC \), \( CA \), and \( AB \) are:
- \( PL = 14 \, \text{cm} \)
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