In the figure above, the area of the parallelogram is
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A. \(40\)
B. \(24\sqrt3\)
C. \(72\)
D. \(48\sqrt3\)
E. \(96\)
Answer: D
Source: Official Guide
Area of parallelogram is base x height
To find the height, drop an altitude to the base. This would form a 306090 triangle, so sides would be in the ratio 1: \(\sqrt{3}\) :2
Thus, \(\sqrt{3}\) :2 = h:8
h =4 \(\sqrt{3}\)
Area = 4 \(\sqrt{3}\) X 12
= 48 \(\sqrt{3}\)
To find the height, drop an altitude to the base. This would form a 306090 triangle, so sides would be in the ratio 1: \(\sqrt{3}\) :2
Thus, \(\sqrt{3}\) :2 = h:8
h =4 \(\sqrt{3}\)
Area = 4 \(\sqrt{3}\) X 12
= 48 \(\sqrt{3}\)
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Solution:Gmat_mission wrote: ↑Thu Sep 24, 2020 2:50 am20190426_1721.png
In the figure above, the area of the parallelogram is
A. \(40\)
B. \(24\sqrt3\)
C. \(72\)
D. \(48\sqrt3\)
E. \(96\)
Answer: D
Source: Official Guide
By drawing the altitude, we see that we have a 306090 triangle nested in the parallelogram, with 8 as the hypotenuse and the altitude as the side opposite the 60degree angle. Since the ratio of the sides of a 306090 triangle is x : x√3 : 2x, the base of the triangle will be x = 4, the altitude will be x√3 = 4√3, and the hypotenuse will be 2x = 8.
Therefore, the area of the parallelogram is base x height = 12 x 4√3 = 48√3.
Answer: D
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