In the figure above, the area of the parallelogram is

Question

https://gmatclub.com/forum/download/file.php?id=47595 In the figure above, the area of the parallelogram is A. 40 B. 24\sqrt{3} C. 72 D. 48\sqrt{3} E. 96 PS50602.01 Quantitative Review 2020 NEW QUESTION 2019-04-26_1721.png

BrentGMATPrepNow · Accepted Answer

Area of parallelogram = (base)(height)

Start by drawing an extra line, which also happens to be the  height  of the parallelogram 
 https://i.imgur.com/hvCAERn.png 
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, . . . 
 https://i.imgur.com/gxmELZJ.png 
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
 https://i.imgur.com/OantROa.png

Area of parallelogram = (base)(height) 
= (12)(4√3)
= 48√3

Answer: D

EgmatQuantExpert · Answer

Solution 
  Given  
In this question, we are given
 • The diagram of a parallelogram, where the adjacent sides are of length 8 and 12
• One angle between the sides is 60°

To Find  
We need to determine
 • The area of the parallelogram

Approach & Working

https://e-gmat.com/blogs/wp-content/uploads/2019/05/85.2.png

Let us assume the parallelogram is PQRS, and QT is the perpendicular dropped from point Q to the side PS.
 • Hence, we can say that PQT is a 30°-60°-90° triangle, and the side ratio is 1: √3: 2.
• QT: PQ = √3: 2
Or, QT = (√3)/2 * PQ = (√3)/2 * 8 = 4√3

• Therefore, the area of the quadrilateral = PS * QT = 12 * 4√3 = 48√3 (PS = QR) 
Hence, the correct answer is option D.

https://e-gmat.com/blogs/wp-content/uploads/2016/12/Geometry-Ability-Quiz-4-e1480581478957.png

nick1816 · Answer

Area of parallelogram= (product of adjacent sides) sinx
 = 8*12*sin60= 96* =48 (3^1/2)

ScottTargetTestPrep · Answer

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 the side opposite the 60-degree angle. Since the ratio of the sides of a 30-60-90 triangle is 1:√3:2, the altitude will be 4√3.

Therefore, the area of the parallelogram is base x height = 12 x 4√3 = 48√3.

Answer: D

dave13 · Answer

BrentGMATPrepNow if parallelogram has sides equal as those of rectangle why simply transforming parallelogram into rectangle and multiplying length by width wont work to find out area of parallelogram? i remember that in some cases one can transform figures but cant remember in what cases such trick works

Any idea ?

Any idea ?

BrentGMATPrepNow · Answer

I'm not aware of a simple trick (e.g., one that doesn't involve trig ratios such as sine and cosine) that would accomplish this.

Consider these two parallelograms (aka rhombuses) in which all sides have length 1
 https://i.imgur.com/XSnfE9p.png

Basshead · Answer

area of parallelogram = base * height

We already know the base is 12; we only need to determine the height.

The left hand side is a 30:60:90 triangle, giving us a ratio of  1:\sqrt{3}:2

Since the hypotenuse is 8, we can conclude that the height of the parallelogram will be  4\sqrt{3}

4\sqrt{3} * 12 = 48\sqrt{3}

Answer is D.

MHIKER · Answer

Are of Parallelogram =  base * height

The base 12 and according to Pitharorian formula of 60-30-90 angle the height  (QT)  is  4\sqrt{3}

So, the  area=    12 * 4\sqrt{3}   =   48\sqrt{3}

The answer is D

poomolb · Answer

area of parallelogram = base * height

We already know the base is 12; we only need to determine the height.

a ratio of 1:3√:21:3:2

the hypotenuse is 8 = height of the parallelogram will be 43√43

43√∗12=483√43∗12=483

Answer is D.

ThatDudeKnows · Answer

The geometry on this one is pretty easy, but just for the sake of argument, let's say you have a total freak-out moment and forget 30-60-90s or that you're short on time. Orrrrrrr that you believe in ballparking as a strategy that helps you do better on the GMAT!!

The area of a parallelogram is base times height. The base is 12. What about the height? Well, we know that the diagonal side is 8. So, is the height 8? No, it's less than 8. How much less than 8? A lot less or just a little less? Just a little less. Okay, let's use 7. Cool, the area is ~12*7 = ~84. We need something between C and E. Answer choice D. LOL at math. ThatDudeKnowsBallparking

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In the figure above, the area of the parallelogram is

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In the figure above, the area of the parallelogram is

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