Here's one solution: https://www.beatthegmat.com/triangle-ins ... 90961.html

Brent@GMATPrepNow wrote:
Answer: D

Here's another solution:

The area of the circle = (pi)(r²) = (pi)(2²), which equals 4(pi)
Since pi = 3.14 (approximately), we know that the area of the circle is APPROXIMATELY 12.

Now, if you had to ESTIMATE at the area of the triangle, what would you say?
Well, it looks like it takes up about half of the space of the circle. So, the area of the triangle is APPROXIMATELY 6.
Now, this isn't a very precise technique, so we might consider a RANGE of possible answers.
Let's be generous and say the area of the triangle is between 4 and 8. Or perhaps even between 3 and 9.
Or, we can be super generous and say the area of the triangle is BETWEEN 2 and 10.

Now let's check the answer choices.

ASIDE: For the GMAT, it's useful to memorize the approximate values of three common roots:
√2 = 1.4
√3 = 1.7
√5 = 2.2

A) (√2)/2 : this is less than 1 . . . way out of range, so ELIMINATE it.
B) √2 : this is about 1.4 . . . way out of range, so ELIMINATE it.
C) √3 : this is about 1.7 . . . way out of range, so ELIMINATE it.
D) 3(√3) : this is about 5.1 . . . within range, so KEEP it.
E) 10(√3) : this is about 17 . . . out of range (in fact, it's bigger than the circle!), so ELIMINATE it.

Answer: D

Cheers,