Question

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)

Answer 1

This is a multiple choice question and the options confusing me

\[a. \frac{ 100 }{ 3 } \\
b. \frac{ 100 }{ 2 } \\
c. \frac{ 125 }{ 3 } \\
d. \frac{ 125 }{ 2 } \\
e. \frac{ 125 }{ 4 } \]

Answer 2

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

Answer 3

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

Answer 4

sorrry gotta go

Answer 5

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

Answer 6

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

Answer 7

so as an inspired guess the answer is C

Answer 8

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