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Herons formula importance?

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billionaire999
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Herons formula importance? [#permalink] New post   29 Mar 2021, 02:46
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Herons formula

A method for calculating the area of a triangle when you know the lengths of all three sides.

Let a,b,c be the lengths of the sides of a triangle. The area is given by:
Area = \sqrt{p ( p − a ) ( p − b ) ( p − c ) }
where p is half the perimeter, or
(a + b + c )/2

I have come across a data sufficiency question, wherein the 3 sides of the triangle are know, and through some time consuming working we can find the height and hence the area of the triangle.

The solution suggested that through the above mentioned herons formula there is no need to work moe, but rather consider the area can be found just by having the dimensions of the 3 sides of the triangle.


Is the formula worthy of the Time?

Please suggest
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Re: Herons formula importance? [#permalink] New post   29 Mar 2021, 07:45
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I have not seen any official question, in which you have to apply this formula.

Remember :
1) If you know 3 sides of the triangle , you can find the area.
2) if you know 2 sides and area of the triangle, you cannot find the third side.


billionaire999 wrote:
Herons formula

A method for calculating the area of a triangle when you know the lengths of all three sides.

Let a,b,c be the lengths of the sides of a triangle. The area is given by:
Area = \sqrt{p ( p − a ) ( p − b ) ( p − c ) }
where p is half the perimeter, or
(a + b + c )/2

I have come across a data sufficiency question, wherein the 3 sides of the triangle are know, and through some time consuming working we can find the height and hence the area of the triangle.

The solution suggested that through the above mentioned herons formula there is no need to work moe, but rather consider the area can be found just by having the dimensions of the 3 sides of the triangle.


Is the formula worthy of the Time?

Please suggest
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GmatKnightTutor
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Re: Herons formula importance? [#permalink] New post   29 Mar 2021, 07:56
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Absorbing the "meaning" of the formula may be helpful at least.
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Re: Herons formula importance? [#permalink] New post   29 Mar 2021, 08:26
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Hi billionaire999
You need not calculate the area of the triangle but only need to make sure that a unique triangle is formed. A unique triangle will have a unique area.
A unique triangle will be produced if you are given:
1. all three sides (Side-Side-Side)
2. two sides and the included angle (Side-Angle-Side)
3. two angles and the included side (Angle-Side-Angle)

billionaire999 wrote:
Herons formula

A method for calculating the area of a triangle when you know the lengths of all three sides.

Let a,b,c be the lengths of the sides of a triangle. The area is given by:
Area = \sqrt{p ( p − a ) ( p − b ) ( p − c ) }
where p is half the perimeter, or
(a + b + c )/2

I have come across a data sufficiency question, wherein the 3 sides of the triangle are know, and through some time consuming working we can find the height and hence the area of the triangle.

The solution suggested that through the above mentioned herons formula there is no need to work moe, but rather consider the area can be found just by having the dimensions of the 3 sides of the triangle.


Is the formula worthy of the Time?

Please suggest
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billionaire999
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Re: Herons formula importance? [#permalink] New post   29 Mar 2021, 10:48
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GMATBusters wrote:
I have not seen any official question, in which you have to apply this formula.

Remember :
1) If you know 3 sides of the triangle , you can find the area.
2) if you know 2 sides and area of the triangle, you cannot find the third side.


billionaire999 wrote:
Herons formula

A method for calculating the area of a triangle when you know the lengths of all three sides.

Let a,b,c be the lengths of the sides of a triangle. The area is given by:
Area = \sqrt{p ( p − a ) ( p − b ) ( p − c ) }
where p is half the perimeter, or
(a + b + c )/2

I have come across a data sufficiency question, wherein the 3 sides of the triangle are know, and through some time consuming working we can find the height and hence the area of the triangle.

The solution suggested that through the above mentioned herons formula there is no need to work moe, but rather consider the area can be found just by having the dimensions of the 3 sides of the triangle.


Is the formula worthy of the Time?

Please suggest



Thanks it helps
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Re: Herons formula importance? [#permalink] New post   15 Dec 2023, 13:16
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It is always better to know and remember if one can.

But since the formula seems complex, just remember that" if you know 3 sides of a triangle you can find the area but if you know area and 2 sides of the triangle, you can't find the third side."

Happy Learning

MaryGrosy wrote:
GMATBusters wrote:
I have not seen any official question, in which you have to apply this formula.

Remember :
1) If you know 3 sides of the triangle , you can find the area.
2) if you know 2 sides and area of the triangle, you cannot find the third side.


billionaire999 wrote:
Herons formula

A method for calculating the area of a triangle when you know the lengths of all three sides.

Let a,b,c be the lengths of the sides of a triangle. The area is given by:
Area = \sqrt{p ( p − a ) ( p − b ) ( p − c ) }
where p is half the perimeter, or
(a + b + c )/2

I have come across a data sufficiency question, wherein the 3 sides of the triangle are know, and through some time consuming working we can find the height and hence the area of the triangle.

The solution suggested that through the above mentioned herons formula there is no need to work moe, but rather consider the area can be found just by having the dimensions of the 3 sides of the triangle.


Is the formula worthy of the Time?

Please suggest



Thanks it helps


But I’m sitting here looking through it and can’t understand.[/quote]

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Re: Herons formula importance? [#permalink] New post   15 Dec 2023, 13:41
I went ahead and memorized it prior to testing but I only ever saw it on like 1-2 questions throughout studies and I think they were both GMATclub questions.

I can’t imagine you will see it on an official.

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Re: Herons formula importance? [#permalink]
15 Dec 2023, 13:41
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