chihiroasleaf
  • chihiroasleaf
ABCD is a square inside a circle. AC is the diagonal of the square and also the diameter of the circle. AE = EB. If the area of the circle is 157. What is the area of quadrilateral BCFE? (picture in comment)
Mathematics
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SOLVED
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chestercat
  • chestercat
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chihiroasleaf
  • chihiroasleaf
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chihiroasleaf
  • chihiroasleaf
This is a multiple choice question and the options confusing me \[a. \frac{ 100 }{ 3 } \\ b. \frac{ 100 }{ 2 } \\ c. \frac{ 125 }{ 3 } \\ d. \frac{ 125 }{ 2 } \\ e. \frac{ 125 }{ 4 } \]
welshfella
  • welshfella
hmm not sure how to do this.. we can work out the radius of the circle pi r^2 = 156 r^2 = 157/pi = 49.97 r = 7.07 so the area of triangle ACB = 0.5 * 7.07*7.07 = 25

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welshfella
  • welshfella
no sorry that is 7.07 * 7.07 = 50 for the area of the triangle
welshfella
  • welshfella
sorrry gotta go
welshfella
  • welshfella
all i can say is that the area of triangle AFE is < 25 so area of BCFE is > 25 and < 50 so that rules out b and d
welshfella
  • welshfella
the area of the square is 100 so AB = 10 and BE = 5 the height of triangle AEF looks about 3 1/3 (i'm making estimates now!) - not exact math!! so the area of AFE us about 3 1/3 * 2.5 = about 8 making the area of BCFE = 50 - 8 = 42
welshfella
  • welshfella
so as an inspired guess the answer is C
welshfella
  • welshfella
there is probably an exact way to do it but I can't see it.

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