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In the figure above, triangle MNO is equilateral. What is the area of

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In the figure above, triangle MNO is equilateral. What is the area of  [#permalink]

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New post 13 Nov 2018, 01:19
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In the figure above, triangle MNO is equilateral. What is the area of triangle MNO ?


(1) NP has a length of \(5\sqrt{3}\).

(2) MN has a length of 10.


Attachment:
2018-11-13_1215.png
2018-11-13_1215.png [ 33.02 KiB | Viewed 705 times ]

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In the figure above, triangle MNO is equilateral. What is the area of  [#permalink]

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New post 13 Nov 2018, 01:30
Bunuel wrote:
In the figure above, triangle MNO is equilateral. What is the area of triangle MNO ?


(1) NP has a length of \(5\sqrt{3}\).

(2) MN has a length of 10.


Attachment:
2018-11-13_1215.png


(D) is our answer.

There are two different approaches to solving this question.
A Precise approach relies on knowledge of geometric rules:
(1) NP is a leg in a 30-60-90 triangle NPO meaning we can calculate the hypotenuse (which is the side of the triangle). Then we have the height and base of a triangle and can calculate its area.
(2) a useful equation to remember is that the area of an equilateral triangle is \(\frac{a^2\sqrt{3}}{4}\), where 'a' is the length of a side.
(Remember 1-2-3-4 i.e. length - square - sqrt(3) - div by 4)

Then both are sufficient.

A second approach, which does not rely on knowledge of geometric rules is Alternative.
An equilateral triangle is a regular polygon and there is only ONE way to draw a regular polygon.
That is - once you know the length of just one of the sides/heights/chords/etc. you know all of the shape's properties. (Try it out - you can SEE this)
So both (1) and (2) are sufficient.
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In the figure above, triangle MNO is equilateral. What is the area of  [#permalink]

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New post 13 Nov 2018, 02:02
Bunuel wrote:
Image
In the figure above, triangle MNO is equilateral. What is the area of triangle MNO ?


(1) NP has a length of \(5\sqrt{3}\).

(2) MN has a length of 10.


Attachment:
2018-11-13_1215.png


The area of equilateral triangle is = \(s^2 *\sqrt{3}/4\)

where the height is\(s * \sqrt{3}/2\)

30:60:90
\(s:s\sqrt{3}:2s\)

we know the height is the side that corresponds to the 60 angle so \(s\sqrt{3} = 5\sqrt{3}\)

From that we can find the side s = 5 and accordingly find the area of the triangle.

Statement 1 is sufficient.

For statement 2

We are given a side of the equilateral triangle so using the equation we can find the area.

Sufficient.

Answer choice D
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Re: In the figure above, triangle MNO is equilateral. What is the area of  [#permalink]

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New post 13 Nov 2018, 03:50
Bunuel wrote:
Image
In the figure above, triangle MNO is equilateral. What is the area of triangle MNO ?


(1) NP has a length of \(5\sqrt{3}\).

(2) MN has a length of 10.


Attachment:
2018-11-13_1215.png


No need of calculating the answer , we just need to check whether given information in statements is sufficient to answer the question or not.

stmnt1: using formula height of triangle= a* (sqrt 3/2)

we can solve for 'a' side of triangle and find area

sufficient

stmnt 2: one side letgh is given area of equilateral triangle would be sqrt 3 a^2/4

sufficient

D is correct option..
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Re: In the figure above, triangle MNO is equilateral. What is the area of  [#permalink]

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New post 15 Nov 2018, 17:18
Is the answer b bc you dont know that NP is perpendicular to the base?
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Re: In the figure above, triangle MNO is equilateral. What is the area of  [#permalink]

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New post 15 Nov 2018, 17:20
Hi Bunuel is the OA of this question B?
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In the figure above, triangle MNO is equilateral. What is the area of  [#permalink]

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New post 15 Nov 2018, 17:27
nn571 wrote:
Is the answer b bc you dont know that NP is perpendicular to the base?


Hi nn571
statement 1 is not sufficient because we don't know that NP is perpendicular to the side.

Answer is B only because for an equilateral triangle we can calculate the area using the formula \(\frac{\sqrt{3}a^2}{4}\), here a is side of the triangle.


hope it helps
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Re: In the figure above, triangle MNO is equilateral. What is the area of  [#permalink]

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New post 15 Nov 2018, 18:38
How do you know NP is not the height?

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Re: In the figure above, triangle MNO is equilateral. What is the area of  [#permalink]

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New post 04 Mar 2019, 19:04
Can someone post the official explanation?
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Re: In the figure above, triangle MNO is equilateral. What is the area of  [#permalink]

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New post 04 Mar 2019, 19:27
The answer is B.... There's no where mentioned in the question that NP is perpendicular to MO...
The right answer is B.... D is a well said trap Answer.

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Re: In the figure above, triangle MNO is equilateral. What is the area of   [#permalink] 04 Mar 2019, 19:27
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In the figure above, triangle MNO is equilateral. What is the area of

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