Area of an equilateral triangle | Perimeter, area, and volume | Geometry | Khan Academy

TL;DR

The video explains how to calculate the area of an equilateral triangle using its side length.

Transcript

Let's say that this triangle right over here is equilateral, which means all of its sides have the same length. And let's say that that length is s. What I want to do in this video is come up with a way of figuring out the area of this equilateral triangle, as a function of s. And to do that, I'm just going to split this equilateral in two. I'm jus... Read More

Key Insights

• 🙃 An equilateral triangle has all sides of equal length.
• 🔺 The altitude of an equilateral triangle bisects one side, creating two 30-60-90 triangles.
• 🔺 The side opposite the 60 degree angle in an equilateral triangle is equal to the side length multiplied by the square root of 3.

Questions & Answers

Q: What is an equilateral triangle?

An equilateral triangle is a triangle in which all three sides have the same length.

Q: How can the area of an equilateral triangle be calculated?

The area of an equilateral triangle can be calculated using the formula: (Square root of 3/4) multiplied by the square of the side length.

Q: How are the side lengths of an equilateral triangle related to each other?

In an equilateral triangle, the side lengths are equal, and the altitude bisects one side, creating two 30-60-90 triangles.

Q: What is the relationship between the side lengths and angles in an equilateral triangle?

In an equilateral triangle, all angles are 60 degrees, and the side opposite the 60 degree angle is equal to the side length multiplied by the square root of 3.

Summary & Key Takeaways

• An equilateral triangle has all sides of equal length.

• By splitting the equilateral triangle and using the properties of a 30-60-90 triangle, the side lengths can be determined.

• The area of an equilateral triangle can be calculated using the formula: (Square root of 3/4) multiplied by the square of the side length.