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 introducing the problem and explaining the properties of a square and a 45-45-90 triangle. The instructor then demonstrates how to calculate the side length of the square using the diagonal and the properties of the triangle. Finally, the video shows how to use the side length to calculate the area of the square and provides practice problems for further learning.

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

• 4

• 6

• 5

• 7

Tags

CCSS.HSG.CO.C.10

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

• 45-45-90

• 90-90-90

• 60-60-60

• 30-60-90

Tags

CCSS.8.G.B.8

How do you express the hypotenuse in terms of the side length in a 45-45-90 triangle?

• x/2

• 2x

• x√2

• x

Tags

CCSS.8.G.B.8

What is the side length of the square if the diagonal is 6?

• 6√2

• 3

• 3√2

• 6

What is the first step in rationalizing the denominator when dividing by √2?

• Multiply by 2

• Multiply by √2/√2

• Divide by 2

• Add √2

Tags

CCSS.3.MD.C.7B

CCSS.4.MD.A.3

What is the area of the square when the side length is 3√2?

• 9

• 12

• 18

• 24

Tags

CCSS.8.EE.A.2

What happens to the square root when you square it?

• It cancels out

• It doubles

• It remains the same

• It halves

Tags

CCSS.3.MD.C.7B

CCSS.4.MD.A.3

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

• side - side

• side ÷ side

• side × side

• side + side

What is the result of squaring 3 in the context of finding the area?

• 15

• 12

• 9

• 6

Tags

CCSS.3.MD.C.7B

CCSS.4.MD.A.3

What should you do after finding the side length to determine the area?

• Divide the side length by 2

• Add the side length

• Square the side length

• Multiply the side length by 2

Tags

CCSS.3.MD.C.7B

CCSS.4.MD.A.3