In the figure above, the area of the parallelogram is

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Thu Sep 24, 2020 2:50 am

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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

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Source: Beat The GMAT — Problem Solving | Thu Sep 24, 2020 2:50 am

psarma: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Wed Jun 29, 2011 1:47 am

Re: In the figure above, the area of the parallelogram is

by psarma » Thu Sep 24, 2020 3:20 pm

Area of parallelogram is base x height
To find the height, drop an altitude to the base. This would form a 30-60-90 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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Re: In the figure above, the area of the parallelogram is

by Scott@TargetTestPrep » Thu Oct 01, 2020 9:55 am

Gmat_mission wrote: ↑
Thu Sep 24, 2020 2:50 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

Solution:

By drawing the altitude, we see that we have a 30-60-90 triangle nested in the parallelogram, with 8 as the hypotenuse and the altitude as the side opposite the 60-degree angle. Since the ratio of the sides of a 30-60-90 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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