In the figure above, the area of the parallelogram is
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B
C
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E
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A. \(40\)
B. \(24\sqrt3\)
C. \(72\)
D. \(48\sqrt3\)
E. \(96\)
Answer: D
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Area of parallelogram = (base)(height)
Start by drawing an extra line, which also happens to be the height of the parallelogram
This creates a special 30-60-90 right triangle
When we compare the blue 30-60-90 right triangle with the purple BASE 30-60-90 right triangle, . . .
We see that the blue 30-60-90 right triangle is 4 times bigger than the purple BASE 30-60-90 right triangle, . .
So, the missing lengths are 4 and 4√3
At this point, we know the base and the height
Area of parallelogram = (base)(height)
= (12)(4√3)
= 48√3
Answer: D