A square, with perimeter 16, is inscribed in a circle. What is the are

Question

A square, with perimeter 16, is inscribed in a circle. What is the area of the circle?

A. 4π
B. 8π
C. 12π
D. 16π
E. 32π

Praveengeol · Answer

Area of circuscribed circle = pi/2*area of square 
Area of square = (16/4)^2 = 4^2= 16 
Area of circle = pi/2*16=8pi

Answer B

Abhishek009 · Answer

Since the Square is inscribed in a circle the vertext of the square touches the circle , further opposite faces (diagonals) touches the Circumferenceof the Circle and forms the Diameter (From which we can obtain the radius and find the area of the circle)

4a = 16

So,  a = 4

Diagonal of the square is  4\sqrt{2}  So, radius of the circle is  4\sqrt{2}

Thus, Area of the circle will be  π*2\sqrt{2}*2\sqrt{2}=8π  , Answer must be (B)

Kinshook · Answer

Side of square = 16/4 = 4
Diagonal of the square =  4\sqrt{2}  = 2r
r =  2\sqrt{2}

Area of the circle =  \pi * (2\sqrt{2})^2 = \pi *8

IMO B

ScottTargetTestPrep · Answer

Since the perimeter is 16, each side is 4, so the diagonal of the square is 4√2. Since the diagonal of the square and the diameter of the circle are equal, the diameter is 4√2, and thus the radius of the circle is ½ x 4√2 =2√2.

Thus, the area of the circle is π(2√2)^2 = 8π.

Answer: B

A square, with perimeter 16, is inscribed in a circle. What is the are

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GMAT Problem Solving (PS) Questions

A square, with perimeter 16, is inscribed in a circle. What is the are

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