Understanding Equilateral Triangles

The video tutorial explains how to calculate the area of an equilateral triangle as a function of its side length, s. It begins by introducing the concept of an equilateral triangle and the goal of finding its area. The triangle is split into two 30-60-90 triangles by dropping an altitude, which bisects the top angle and the base. The properties of 30-60-90 triangles are used to determine the altitude, which is crucial for calculating the area. The area is then calculated using the formula 1/2 times the base times the height, resulting in a general formula for the area of an equilateral triangle.

What is the defining characteristic of an equilateral triangle?

• It has two equal sides

• It has one right angle

• All sides have the same length

• All angles are 90 degrees

What is the purpose of dropping an altitude in an equilateral triangle?

• To split the triangle into two right triangles

• To determine the base length

• To calculate the hypotenuse

• To find the perimeter

In a 30-60-90 triangle, what is the ratio of the sides opposite the 30, 60, and 90 degree angles?

• 1:2:3

• √3:1:2

• 1:√3:2

• 2:1:√3

What happens to the angles when an altitude is drawn in an equilateral triangle?

• They become 90 degrees

• They split into 30 and 60 degrees

• They become 45 degrees

• They remain 60 degrees

What is the length of the altitude in terms of s for an equilateral triangle?

• s

• s/2

• √3 * s/2

• 2s

How do you calculate the area of an equilateral triangle?

• base + height

• 1/3 * base * height

• base * height

• 1/2 * base * height

Why is the altitude important in calculating the area of an equilateral triangle?

• It is used to find the perimeter

• It helps in determining the base

• It divides the triangle into two equal parts

• It is needed to apply the area formula

What is the area of an equilateral triangle with side length 1?

• 1

• √3/4

• 1/2

• √3

If the side length of an equilateral triangle is 2, what is its area?

• 1

• 2√3

• 2

• √3

What is the general formula for the area of an equilateral triangle with side length s?

• s^2

• √3 * s^2 / 4

• s^2 / 2

• √3 * s / 2