Equilateral Triangle Concepts and Calculations

The video tutorial explains how to find the area of an equilateral triangle. It begins by defining an equilateral triangle as one with three equal sides. The tutorial then demonstrates how to calculate the area using the formula: one-half the base times the height. It explains how to find the height by splitting the base and using the 30-60-90 triangle rule. The video also covers how to work backwards from a given altitude to find the side length, using rationalization and multiplication techniques.

What is a defining characteristic of an equilateral triangle?

• It has two equal sides.

• All sides are equal in length.

• It has one right angle.

• All sides are of different lengths.

What is the formula for the area of a triangle?

• Base plus height

• One half base times height

• Base times height

• Base minus height

In an equilateral triangle, how do you find the altitude?

• Divide the base by 2 and multiply by the square root of 3

• Multiply the base by 2

• Add the base and height

• Subtract the base from the height

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

• 5

• 5 square root 3

• 10 square root 3

• 10

How do you calculate the area of an equilateral triangle with a side length of 10?

• 25 square root 3 square units

• 50 square root 3 square units

• 100 square root 3 square units

• 10 square root 3 square units

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

• Divide the altitude by the square root of 3 and double the result

• Subtract the altitude from the base

• Add the altitude to the base

• Multiply the altitude by the square root of 3

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

• 2 square root 3

• 4 square root 3

• 6 square root 3

• 8 square root 3

How do you rationalize the expression 6 divided by the square root of 3?

• Multiply by square root of 3 over square root of 3

• Subtract square root of 3

• Divide by square root of 3

• Add square root of 3

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

• 20 square root 3 square units

• 8 square root 3 square units

• 16 square root 3 square units

• 12 square root 3 square units

What is the process to find the side length from a given altitude in an equilateral triangle?

• Multiply the altitude by 2

• Divide the altitude by the square root of 3 and double the result

• Add the altitude to the base

• Subtract the altitude from the base