Math Is Fun Forum

Monique

Member

Registered: 2007-02-17

Posts: 22

area of the triangle using the perpend. height formula?

if the base of a triangle A to B = 10cm, its opposite side C to B = 8cm and B to A = 6cm, how would I find the area of the triangle using the perpendicular height formula?

desperate Monique!

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,179

Re: area of the triangle using the perpend. height formula?

The area of a trianlge, when the height (or altitude, as referred in some texts) and the base is known is

In the problem you have stated,
the height has not been given.
However, by looking at the lengths of the sides, i.e. 6, 8 and 10 cm, it can be seen that it is a right angled triangle.
This is because 6² + 8² = 36 + 64 = 100 = 10²
(Pythogoras theorem).
Since 10 is the longest side, it is the hypotenuse.
Hence, the area would be
A=1/2 x 6 x 8 = 1/2 x 48 = 24 cm².

However, when only the lenghts of the three sides are given, Hero's formula (or Heron's formula) may be used. According to the formula,

where

and a, b, and c are the three sides.

Using this formula for your problem, we get s= (6+8+10)/2=12
(s-a) = 6, (s-b) = 4 and (s-c) = 2.
Hence Area = √(12x6x4x2)=√576=24 sq.cm.

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Monique

Member

Registered: 2007-02-17

Posts: 22

Re: area of the triangle using the perpend. height formula?

Thanks Ganesh. This is the conclusion I came to as well. Just wasnt sure if I had the right answer. This stuff perhaps begining to make sense after all...

archandis

Guest

Re: area of the triangle using the perpend. height formula?

hello whhat is the height formula
thank you very much

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: area of the triangle using the perpend. height formula?

If you're not already given the height, it can be quite difficult to calculate it.

The method will vary depending on what you are given. If the triangle is iscoceles and you're given all of the sides, then you could cut it in half and use Pythagoras to get the height. If you're given an angle, then some form of trigonometric formula would help.
We can't really explain in more detail without you explaining what the triangle is first.

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Why did the vector cross the road?
It wanted to be normal.