Geometry Quiz: Semicircle and Inscribed Squares

What is the area of the inscribed square in the semicircle?

• 24 square units

• 18 square units

• 36 square units

• 48 square units

If the side of the inscribed square is 6 units, what is half of this side?

• 2 units

• 4 units

• 5 units

• 3 units

What is the hypotenuse of the right triangle formed by the inscribed square?

• 3 units

• 6 units

• 9 units

• 3√5 units

How is the radius of the semicircle related to the hypotenuse of the right triangle?

• It is twice the hypotenuse

• It is half the hypotenuse

• It is equal to the hypotenuse

• It is unrelated

What is the expression for the side of the smaller square?

• x - 3

• x + 3

• 3x

• x

What equation is set up to find the side of the smaller square?

• x^2 + 3x = 0

• x^2 + (x + 3)^2 = (3√5)^2

• x^2 + 6x = 0

• x^2 - 3x = 0

What is the simplified form of the quadratic equation used to find x?

• x^2 - 6x + 36 = 0

• x^2 + 3x - 18 = 0

• x^2 - 3x + 18 = 0

• x^2 + 6x - 36 = 0

What are the possible solutions for x in the quadratic equation?

• x = 3 and x = -6

• x = 0 and x = 3

• x = 6 and x = -3

• x = 9 and x = -9

Why is x = -6 not a valid solution for the side of the square?

• x must be less than 6

• x must be a whole number

• x must be positive

• Negative numbers are not allowed

What is the area of the smaller square?

• 15 square units

• 6 square units

• 9 square units

• 12 square units