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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
A. 4π
B. 8π
C. 12π
D. 16π
E. 32π
Praveengeol
Joined: 02 Jun 2015
Last visit: 14 Nov 2017
Posts: 58
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Given Kudos: 27
Location: United States
Concentration: Strategy, Human Resources
Schools: Schulich Sept"18 (A)
WE:Engineering (Manufacturing)
10 Jan 2016, 09:15
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Bunuel
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
A. 4π
B. 8π
C. 12π
D. 16π
E. 32π
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
12 Sep 2019, 08:26
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Bunuel
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
A. 4π
B. 8π
C. 12π
D. 16π
E. 32π
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)
