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Given a triangle ABC. What is the area? 1. the triangle has

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Given a triangle ABC. What is the area? 1. the triangle has [#permalink] New post 16 Oct 2004, 09:38
Given a triangle ABC. What is the area?


1. the triangle has the following sides 5,12,13

2. the triangle has the following sides 5,6,7
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 [#permalink] New post 16 Oct 2004, 09:46
Use the semi-perimeter to calculate the area of the triangle:

s = semiperimeter = (a+b+c)/2

Area = SQRT [s(s-a)(s-b)(s-c)]
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 [#permalink] New post 16 Oct 2004, 09:49
1. Represents a Pythagorean triplet and the area would be 1/2*12*5 = 30

2. semiperimeter S = 18/2 = 9.
Area = sqrt[9(9-5)(9-6)(9-7)] = sqrt[216] = 14.70.
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 [#permalink] New post 16 Oct 2004, 10:54
I never heard of this formula.
Can you really calculate the area of any triangle without knowing it's base and height ?

Are we expected to know this formula ?
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 [#permalink] New post 16 Oct 2004, 11:14
Interesting formula indeed. Thanks all, I put this in my favorites and I believe having read this somewhere in this club a long time ago but did not pay much attention to it. This seems like a realistic DS question to me.

Below is a link to that formula
http://www.murderousmaths.co.uk/books/BKMM5xar.htm
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 [#permalink] New post 16 Oct 2004, 11:37
Oh! this is a popular formula in India atleast. Couple of other ones while on the subject...

1. For a equilateral triangle:
area = [sqrt(3)/4] * (side)^2. And the altitude or height h = sqrt(3)/2 * (side)

2. For an isoceles triangle,
Area = (c/4)*sqrt[(4a^2-c^2)]. 'a'=length of one of the two sides that are equal and 'c' is the length of the third side.

In a isoceles triangle, hypotenuse = sqrt(2)*(length of the equal side).
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 [#permalink] New post 16 Oct 2004, 12:07
I would guess that the Hero's Formula, Area = SQRT [s(s-a)(s-b)(s-c)], named after the Hero of Alexandria, though interesting, is outside the scope of GMAT as far as PS questions are concerned! But yes it could be wrapped up in a DS question - testing knowledge of it rather than how to apply it.
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 [#permalink] New post 16 Oct 2004, 14:49
It is never meant to use Hero's formula

The logic is that 3 sides are enough for the area. we have one and only one triangle having this figure

we can find area if we know either one of the following:
3 sides
2 sides included angle
2 angles and a side
or base and height

In a DS question,we aught to see if we can find it or not,not to solve it.

For those who know Hero of Alexandria, it is a plus. :)
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 [#permalink] New post 17 Oct 2004, 09:07
That's a good forumula, I haven't used it but I figured that if we knew all the sides of a triangle, there's only one possible area for this triangle and there must be a genius out there have a forumla for this...

So the answer is D
  [#permalink] 17 Oct 2004, 09:07
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