Monday, June 22, 2009
Hi TianChong here =] Today i am going to talk about the areas of triangles.Ok lets first start off today by asking.. How many formulas do you all know?
Well the most basic ones that any student who studied mathematics up to high school will probably know : Area = 1/2 x base x height
or by using another commonly used method, trigonometry: Area = 1/2 absinC
So now, i am going to talk about some other methods that are not commonly used such as by using coordinates :
If vertex A is located at the origin (0, 0) of a Cartesian coordinate system and the coordinates of the other two vertices are given by B = (xB, yB) and C = (xC, yC), then the area S can be computed as ½ times the absolute value of the determinant
Hence, Area = 1/2 det [abs( xB xC )]
___________________[abs( yB yC )]
or for three general vertices, the formula is :
Area = 1/2 det [abs( xA xB xC )]
_____________[abs( yA yB yC )]
_____________[abs( 1 1 1 )]
In addition, there is also a method by using vectors:
The area of triangle ABC can also be expressed in terms of dot products
Area = 1/2{sqr root[(AB.AB)(AC.AC) - (AB.AC)sqr]}
Lastly, there is the Heron's formula :
The shape of the triangle is determined by the lengths of the sides alone. Therefore the area also can be derived from the lengths of the sides.
By Heron's formula:
Area = {sqr root[s(s - a)(s - b)(s - c)]}
where s = ½ (a + b + c) is the semiperimeter, or half of the triangle's perimeter.
Yup these formulas are pretty useful huh =D thats all happy mathematic-ing
acknowledgement : wikipedia
Xiao Yuting
Wan Tian Chong
