Understanding Equilateral Triangles

The video tutorial explains how to find the area of an equilateral triangle. It begins by defining an equilateral triangle and assigning a side length of 10. The tutorial then demonstrates how to calculate the area using the formula for the area of a triangle, which is one-half the base times the height. It explains how to find the height using the properties of a 30-60-90 triangle. The video also covers how to work backwards from a given altitude to find the side length of the triangle. This involves dividing the altitude by the square root of 3 and rationalizing the result.

What is a defining characteristic of an equilateral triangle?

• It has two equal angles.

• It has one right angle.

• It has three equal sides.

• It has two equal sides.

What formula is used to find the area of a triangle?

• Base plus height

• Base minus height

• One-half base times height

• Base times height

How do you find the height of an equilateral triangle?

• Divide the base by 2

• Add the base and height

• Multiply the base by the square root of 3

• Use the 30-60-90 triangle rule

What is the height of an equilateral triangle with a side length of 10?

• 10√3

• 10

• 5

• 5√3

What is the area of an equilateral triangle with a side length of 10?

• 50√3 square units

• 50 square units

• 25 square units

• 25√3 square units

If given the altitude of an equilateral triangle, how can you find the side length?

• Subtract the altitude from the base

• Divide the altitude by the square root of 3

• Multiply the altitude by 2

• Add the altitude to the base

What is the side length of an equilateral triangle if the altitude is 6?

• 6√3

• 4√3

• 2√3

• 8√3

How do you rationalize the expression 6/√3?

• Add √3

• Divide by √3

• Subtract √3

• Multiply by √3/√3

What is the area of an equilateral triangle with a side length of 4√3?

• 24√3 square units

• 24 square units

• 12√3 square units

• 12 square units

What is the relationship between the altitude and the side length in an equilateral triangle?

• The altitude is half the side length.

• The altitude is the same as the side length.

• The altitude is the side length divided by √3.

• The altitude is the side length multiplied by √3.