## chihiroasleaf one year ago 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)

1. chihiroasleaf

2. chihiroasleaf

This is a multiple choice question and the options confusing me $a. \frac{ 100 }{ 3 } \\ b. \frac{ 100 }{ 2 } \\ c. \frac{ 125 }{ 3 } \\ d. \frac{ 125 }{ 2 } \\ e. \frac{ 125 }{ 4 }$

3. 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

4. welshfella

no sorry that is 7.07 * 7.07 = 50 for the area of the triangle

5. welshfella

sorrry gotta go

6. 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

7. 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

8. welshfella

so as an inspired guess the answer is C

9. welshfella

there is probably an exact way to do it but I can't see it.