Calculating Equilateral Triangle Perimeter from Area

Problem Overview

• 🎯 The video aims to calculate the perimeter of an equilateral triangle ABC.
• 💡 The area of triangle ABC is given as 12 * sqrt(3) cm².
• 🔑 An equilateral triangle has all three sides equal (denoted as 'a') and all interior angles are 60 degrees.

Method 1: Using Equilateral Area Formula

• 📝 The formula for the area of an equilateral triangle is Area = (sqrt(3) * a²) / 4.
• 🔢 By substituting the given area, the equation becomes 12 * sqrt(3) = (sqrt(3) * a²) / 4.
• ✅ Solving for 'a', the side length a is found to be 4 * sqrt(3) cm.

Method 2: Using General Triangle Area Formula

• 📐 This method uses the general area formula: Area = 0.5 * side1 * side2 * sin(angle between them).
• 🧠 For an equilateral triangle, this translates to Area = 0.5 * a * a * sin(60°).
• 💡 Knowing that sin(60°) = sqrt(3) / 2, the equation simplifies to 12 * sqrt(3) = a² * sqrt(3) / 4.
• ⚡️ This leads to the same side length: a = 4 * sqrt(3) cm.

Calculating the Perimeter

• 📏 The perimeter of an equilateral triangle is the sum of its three equal sides, P = 3a.
• ➕ Substituting the calculated side length, P = 3 * (4 * sqrt(3)).
• ✨ The final perimeter of the equilateral triangle is 12 * sqrt(3) cm.