(Q28)Find the area of the triangle formed by the points by using Herons formula.

(1,1) , (1,4) and (5,1)

Let A(1,1) B(1,4) and C(5,1) are the vertices then length of sides can be calculated using the formula

√(x2 - x1)2 + (y2 - y1)2

Now

AB = c = √((-)2 + (-)2)

   = √(2 + ()2)

   = √ + = units

BC = a = √((-)2 + (-)2)

   = √((-)2 + ()2)

   = √ + = √ = units

CA = b = √((-)2 + (-)2)

   = √(()2 + ()2)

   = √ + = √ = units

now formula for area of triangle using Herons formula = ∆ = √(s(s-a)(s-b)(s-c))

Where s =
a+b+c
2
s =
++
2
 =

∆ = √(()( - 5)( - 4)( - 3))

 = sq.units

Area of given triangle = sq.units .