Understanding the Area of a Square with a Given Diagonal

The video tutorial explains how to find the area of a square when given the diagonal length. It begins by discussing the properties of a square and introduces the concept of a 45-45-90 triangle. The tutorial then demonstrates how to calculate the side length of the square using the diagonal and rationalization techniques. Finally, it shows how to use the side length to find the area of the square, resulting in an area of 18 square units.

What is the given diagonal length of the square in the problem?

• 4 units

• 5 units

• 6 units

• 7 units

What type of triangles are formed when a diagonal is drawn in a square?

• Scalene triangles

• Equilateral triangles

• 45-45-90 triangles

• 30-60-90 triangles

In a 45-45-90 triangle, if the hypotenuse is 6, what is the formula to find the side length?

• Hypotenuse * √2

• Hypotenuse / 2

• Hypotenuse * 2

• Hypotenuse / √2

What is the side length of the square derived from the diagonal?

• 5√2

• 6√2

• 4√2

• 3√2

What is the significance of rationalizing the denominator in this problem?

• To calculate the area

• To determine the diagonal

• To simplify the expression

• To find the hypotenuse

How do you calculate the area of a square once you have the side length?

• Multiply the side by 4

• Add the side length to the diagonal

• Square the side length

• Multiply the side by 2

What is the result of squaring the side length 3√2?

• 12

• 9

• 18

• 15

What is the final area of the square with a diagonal of 6 units?

• 12 square units

• 15 square units

• 18 square units

• 21 square units

What happens to the square root when you square 3√2?

• It doubles

• It cancels out

• It triples

• It remains the same