Properties of Equilateral Triangle:

• All three sides are of equal length
• All three angles are equal to 60 degrees
• The altitude, median, and angle bisectors are all the same line in an equilateral triangle
• It has three lines of symmetry
• The area can be calculated using the formula: Area = (s² * (√3))/4, where s is the length of the side
• The perimeter can be calculated using the formula: Perimeter = 3s, where s is the length of the side

Key Concepts:

• Equilateral triangles have special properties due to their regularity
• All equilateral triangles are also isosceles triangles
• They can be used to create tessellations, where they fit together to fill a plane with no overlaps or gaps
• Equilateral triangles are the only type of triangle that can tessellate a plane by themselves

Example Problem:

Calculate the area and perimeter of an equilateral triangle with a side length of 6 cm.

Solution:

Given side length s = 6 cm

Using the area formula: Area = (s² * (√3))/4

Area = (6² * (√3))/4

Area = (36 * (√3))/4

Area = 9√3 square cm

Using the perimeter formula: Perimeter = 3s

Perimeter = 3 * 6

Perimeter = 18 cm

Practice Problems:

1. Find the area and perimeter of an equilateral triangle with a side length of 8 units.
2. Determine the altitude of an equilateral triangle with a side length of 10 cm.
3. If the perimeter of an equilateral triangle is 24 inches, find the length of each side.