Vincen wrote: ↑

Sat Dec 04, 2021 7:41 am

2019-04-26_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

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