Friday, April 9, 2010

How to find area of a triangle

Triangle is a plane figure bounded by three straight lines. A triangle may have three sides unequal, two sides equal and all sides equal. The triangles with all sides unequal are called scalene triangles; the triangles with two sides equal are called isosceles triangles and the triangle with three sides equal is called as equilateral triangles. The area of any triangle is equal to half of the base and altitude (A = (base * height)/2). The area of an equilateral triangle, A= ((sqrt 3)/4) * square of side. The area of scalene triangle, A= sqr.rt. (s(s-a)(s-b)(s-c)). An example is shown below for each type of triangles.

For Equilateral Triangles
  • Consider an equilateral triangle of side 3 cm.

Area= ((sqrt 3)/4) * sq. of side.
Area= (1.732/4) * 9
Area= 3.897 sq.cm.

For Isosceles Triangle
  • Consider an isosceles triangle of side AB=2 cm, BC=2 cm, AC=4 cm. Let ‘AB’ be base (b) and ‘BC’ be height (h).

Area= (base * height)/2
Area= (2 * 2)/2
Area= 2 sq.cm.

For Scalene Triangles
  • Consider a scalene triangle of side AB=2 cm (a), BC=3 cm (b), AC=4 cm (c).

S= (a+b+c)/2
Area= sqrt (s (s-a) (s-b) (s-c))
Area= sqrt (4.5 (4.5-2) (4.5-3) (4.5-4))
Area= sqrt (4.5 * 2.5 * 1.5* 0.5)
Area= 2.904 sq.cm.

I hope that you understand how to calculate the area of any type of triangles. Please express your opinions.

No comments: