Question

Find the area of the triangle formed by the points (2,3),(6,3)and (2,6) by using herons formula

Answer 1

Answer:

Let A=(2,3),B=(6,3),C=(2,6)

AB=√(6-2)²+(3-3)²

AB=√(4)²+0

AB=√16=4

BC=√(2-6)²+(6-3)²

BC=√(-4)²+(3)²

BC=√16+9

BC=√25=5

AC=√(2-2)²+(6-3)²

AC=√0+3²

AC=√9=3

Let

AB=c=4

BC=a=5

AC=b=3

Heron's Formula is given by

A=√s(s-a)(s-b)(s-c)

where s=a+b+c/2

s=4+5+3/2

s=12/2

s=6

s-a=6-5=1

s-b=6-3=3

s-c=6-4=2

Area of a triangle, ΔABC

=√6(2)(1)(3)

=√36

=6 square units

Answer 2

Answer:

6 sq units

Step-by-step explanation:

it is area of triangle