Area of triangle

• 1. Area of a triangle when we know the base and the height

     The area of a triangle is equal to half of base times height.

     A =	1	a · h
     	2

  2. Area of a triangle when we know the lengths of all three of its sides (Heron's formula)

     A = √s(s - a)(s - b)(s - c)

  3. Area of a triangle when we know two sides and the included angle

     The area of a triangle is equal to half of a product of two sides and sine of the angle between this sides.

     A =	1	a · b · sin γ
     	2

     A =	1	a · c · sin β
     	2

     A =	1	b · c · sin α
     	2

  4. Area of a triangle when we know three sides and circumradius

     A =	a · b · с
     	4R

  5. Area of a triangle when we know semiperimeter and in-radius

     The area of a triangle is equal to semiperimeter times in-radius.
     

     A = s · r

     
     where A - the area of a triangle,
     a, b, c - the length of sides BC,AC,AB accordingly,
     h - the height, the length of the altitude,
     α, β, γ - the angles,
     r - the length of the in-radius,
     R - the length of the circumradius,
     

     s =	a + b + c	- the semiperimeter, or half of the triangle's perimeter.
     	2

     REFERENCE FROM onlinemschool.com/math/formula/area/