Understanding the Area of a Square

This video tutorial explains how to calculate the area of a square using different methods. It starts with the basic formula of side squared, then explores more complex scenarios like using algebraic expressions for side lengths, calculating area from the perimeter, and using the diagonal length with the Pythagorean theorem. The video also derives a formula relating the area directly to the diagonal.

What is the formula for calculating the area of a square when the side length is known?

• Diagonal squared

• Perimeter divided by four

• Side length squared

• Length times Width

If a square has a side length of 8 feet, what is its area?

• 32 square feet

• 64 square feet

• 16 square feet

• 8 square feet

How do you express the area of a square with a side length of x + 2?

• (x + 2) squared

• x squared plus 4

• x plus 2

• x times 2

What is the expanded form of (x + 2) squared?

• x squared plus 4x plus 4

• x squared plus 4

• x squared plus 2x plus 2

• x squared plus 2

Given a square with a perimeter of 32 units, what is the side length?

• 4 units

• 8 units

• 16 units

• 32 units

How do you calculate the area of a square if the perimeter is known?

• Divide the perimeter by 4 and square the result

• Multiply the perimeter by 4

• Divide the perimeter by 2

• Square the perimeter

What is the area of a square with a diagonal length of 100 inches?

• 1,000 square inches

• 2,500 square inches

• 5,000 square inches

• 10,000 square inches

Using the Pythagorean theorem, how is the diagonal of a square related to its side length?

• Diagonal squared equals side length squared

• Diagonal squared equals twice the side length squared

• Diagonal equals side length

• Diagonal equals twice the side length

What is the formula for the area of a square in terms of its diagonal?

• Half the square of the diagonal

• Twice the square of the diagonal

• Diagonal squared

• Diagonal divided by two

If the diagonal of a square is 100 inches, what is the area using the derived formula?

• 5,000 square inches

• 10,000 square inches

• 1,000 square inches

• 2,500 square inches