I keep ending up with 6 - πx^2. Could someone help explain how to do this problem? I am almost there but am doing something wrong since I keep ending up with this answer. Any insight would be appreciated. Thank you!
goodyear2013 wrote:
A circular region centered at C is inscribed in equilateral triangle ABC above. If the area of ΔABC is 12, then what is the area of the shaded region?
A. 6-3π
B. 6-π√3
C. 12-π√3
D. 12-3π
E. 3+π√3
One could also use following approach and solve this question in 30 seconds:
The area of the shaded region = 1/2*(the area of the triangle - the area of the sector) = 1/2*(12 - something with π) = 6 - something with π.
Only A and B fits this format, but A is negative, so we can discard it.
Also:
C: 12 - π√3 = ~7 too big for the area of the tiny shaded region (more than half of the area of the triangle).
D: 12 - 3π = ~3 too big for the area of the tiny shaded region (~1/4 of the area of the triangle).
E: 3 + π√3 = ~8 too big for the area of the tiny shaded region (more than half of the area of the triangle).
Answer: B.