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GMAT Practice Question (One of Hundreds)

What is the area of the triangle pictured above?

A)	24
B)	24
C)	48
D)	48
E)	96

Correct Answer: B

Extend the triangle out to determine the height.

The formula for the area of a triangle is A=(1/2)(b)(h). We know that the base of the triangle is 12, but we are not given the height. To find the area, we must calculate the height.
If we extend the base of the triangle on the right hand side, we can draw a vertical line segment that is the height of our original triangle. In the process, we have created a smaller triangle whose hypotenuse has length 8. This triangle is a 30-60-90 triangle:
1) One of its angles is a right angle, so its measure is 90 degrees.
2) The lower left angle measures 60 degrees, since it is supplementary to a 120 degree angle.
3) Since two of the angles measure 90 degrees and 60 degrees, the third measures 180 - 90 - 60 = 30 degrees.
In a 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg, and so the base of this smaller triangle is 4. The longer leg is equal to the shorter leg times , which in this case gives us a longer leg of 4. This happens to be the height of both triangles.
Looking back to our original triangle, we see that its base is 12 and its height is 4. Therefore its area is given by:
A = (1/2)(b)(h) = (1/2)(12)(4) = 24
The correct answer is B.

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