What is the area of the triangle shown below?

Question

https://gmatclub.com/forum/download/file.php?id=59466 What is the area of the triangle shown below? (A) 5 \sqrt{2} (B) 7.5 (C) \frac{13 \sqrt{3}}{3} (D) \frac{9 \sqrt{3}}{2} (E) 5 \sqrt{3} 2020-12-14_17-48-41.png

Nipungupta9081 · Answer

IMO D

Area = 1/2 * Base * Height
 
 = 1/2 * 3 * 3 √3 = 9 √3 / 2

akadiyan · Answer

The triangle given is 30-60-90, so the sides of the triangle are in ratio x: x\sqrt{3} :2x

Base of triangle is x = 3
We know the side that's height of triangle is 3 \sqrt{3}

Area of triangle =  \frac{Base * Height }{ 2}

=  \frac{3 * 3\sqrt{3} }{ 2} 
=  \frac{9 \sqrt{3} }{2}

Ans   D

CrackverbalGMAT · Answer

SOLUTION:

This is a 30-60-90 triangle , its side lengths are always in the ratio of 1: √3: 2. [a: 3√3 a :2a]
Thus, the altitude is 3√3 units.
Area of a triangle = (1/2)*a*b*sin of the included angle
= (1/2) * 3 * 3√3 * sin90
=(9√3)/2 sq units (OPTION D)

Hope this helps

Devmitra Sen(Math)

kntombat · Answer

In a 30-60-90 triangle, the ratio of the side is  1:√3: 2.
 
Therefore, in this case the side of the triangle are  3: 3√3: 6.

Now the area of a right angle triangle is  \frac{1}{2}*base*height =  \frac{1}{2}*3*3√3 .

Therefore, the area of the triangle is  \frac{9√3}{2.} .

The OA is D.

What is the area of the triangle shown below?

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What is the area of the triangle shown below?

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