Equilateral Triangle Theorem Formula and Examples

📚 Quick Study Guide

📐 An equilateral triangle is a triangle in which all three sides are equal in length. 📏 All three angles in an equilateral triangle are also equal, each measuring 60 degrees. 🧮 The area of an equilateral triangle can be calculated using the formula: $A = \frac{\sqrt{3}}{4} a^2$, where 'a' is the length of a side. 🧭 The perimeter of an equilateral triangle is simply three times the length of one side: $P = 3a$. 🧐 The altitude (height) of an equilateral triangle is given by: $h = \frac{\sqrt{3}}{2} a$, where 'a' is the side length.

Practice Quiz

1. What is the measure of each angle in an equilateral triangle?
   1. 30 degrees
   2. 45 degrees
   3. 60 degrees
   4. 90 degrees
2. If an equilateral triangle has a side length of 4 cm, what is its perimeter?
   1. 8 cm
   2. 12 cm
   3. 16 cm
   4. 20 cm
3. What is the area of an equilateral triangle with a side length of 2 cm?
   1. $\sqrt{3}$ cm$^2$
   2. $2\sqrt{3}$ cm$^2$
   3. $3\sqrt{3}$ cm$^2$
   4. $4\sqrt{3}$ cm$^2$
4. What is the height of an equilateral triangle with a side length of 6 cm?
   1. $2\sqrt{3}$ cm
   2. $3\sqrt{3}$ cm
   3. $4\sqrt{3}$ cm
   4. $5\sqrt{3}$ cm
5. Which of the following statements is NOT true about an equilateral triangle?
   1. All sides are equal.
   2. All angles are equal.
   3. It has one angle of 90 degrees.
   4. It is also an equiangular triangle.
6. If the perimeter of an equilateral triangle is 27 cm, what is the length of each side?
   1. 6 cm
   2. 7 cm
   3. 8 cm
   4. 9 cm
7. The area of an equilateral triangle is $9\sqrt{3}$ cm$^2$. What is the length of each side?
   1. 4 cm
   2. 5 cm
   3. 6 cm
   4. 7 cm