Equilateral Triangle Concepts and Area

This video tutorial explains how to calculate the area of an equilateral triangle. It begins by introducing the properties of equilateral triangles, including congruent sides and angles. The video then presents the formula for calculating the area, which involves the square root of 3 divided by 4 times the side length squared. The tutorial further explains how to derive this formula using the properties of 30-60-90 triangles. By the end, viewers will understand how to apply the formula to find the area of any equilateral triangle.

What is a key characteristic of an equilateral triangle?

• It has one right angle.

• All sides and angles are equal.

• All angles are 90 degrees.

• All sides are different lengths.

Which formula is used to calculate the area of an equilateral triangle with side length 's'?

• s^2 * sqrt(3)

• sqrt(3) / 4 * s^2

• s^2 / 2

• s^2

If the side length of an equilateral triangle is 10, what is the exact area?

• 25 sqrt(3)

• 100

• 25

• 50

What is the measure of each angle in an equilateral triangle?

• 45 degrees

• 60 degrees

• 90 degrees

• 120 degrees

What is the role of the altitude in an equilateral triangle?

• It is not used in area calculation.

• It is equal to the side length.

• It is always outside the triangle.

• It divides the triangle into two congruent triangles.

In a 30-60-90 triangle, what is the length of the side opposite the 30-degree angle if the hypotenuse is 's'?

• s

• s/3

• s/2

• s*sqrt(3)

How is the height of an equilateral triangle related to its side length?

• Height is sqrt(3)/2 times the side length.

• Height is half the side length.

• Height is equal to the side length.

• Height is twice the side length.

What is the purpose of deriving the area formula for an equilateral triangle?

• To find the perimeter.

• To understand the relationship between sides and angles.

• To calculate the area using basic geometry.

• To determine the height.

What is the relationship between the base and height in the area formula of a triangle?

• Base and height are equal.

• Area is half the product of base and height.

• Height is always longer than base.

• Base is always longer than height.

What is the final step in deriving the area formula for an equilateral triangle?

• Using the Pythagorean theorem.

• Multiplying the base and height.

• Calculating the perimeter.

• Dividing by 4.