Equilateral Triangle

An equilateral triangle is a special type of triangle where all three sides are of equal length and all three angles are of equal measure (60 degrees).

Properties of an Equilateral Triangle:

1. Side Lengths: All three sides are of equal length.
2. Angles: All three angles are of equal measure (60 degrees).
3. Perimeter: The perimeter of an equilateral triangle is three times the length of one of its sides.
4. Area: The area of an equilateral triangle can be calculated using the formula: \( \frac{\sqrt{3}}{4} \times \text{side length}^2 \)

Formulas:

• Perimeter: \( \text{Perimeter} = 3 \times \text{side length} \)
• Area: \( \text{Area} = \frac{\sqrt{3}}{4} \times \text{side length}^2 \)

Example Problem:

Find the perimeter and area of an equilateral triangle with a side length of 5 units.

Solution:

Given side length (\( s \)) = 5 units

Perimeter (\( P \)) = \( 3 \times 5 = 15 \) units

Area (\( A \)) = \( \frac{\sqrt{3}}{4} \times 5^2 = \frac{\sqrt{3}}{4} \times 25 \) square units

Key Takeaways:

• An equilateral triangle has all sides of equal length and all angles of equal measure.
• The perimeter is three times the length of one side, and the area can be calculated using the specific formula.
• Understanding the properties and formulas for equilateral triangles is essential for solving problems involving them.

[Equilateral Triangle] Related Worksheets and Study Guides:

• Plane figuresMathematics • Eighth Grade