Given: A triangle ABC with sides AB=4cm, BC=6cm and AC=8cm
Required: To find out the area of the given triangle.
Explanation: Area of the triangle by Heron's formula is given by,
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]where, a,b,c are the sides of triangle and s is the semi-perimeter given by,
[tex]s=\frac{(a+b+c)}{2}[/tex]Now, let a=4, b=6 and c=8. Hence the semi perimeter s is-
[tex]s=\frac{4+6+8}{2}[/tex][tex]s=9\text{ cm}[/tex]Now, putting these values of s, a, b, and c in Heron's formula we get,
[tex]A=\sqrt{9(9-4)(9-6)(9-8)}[/tex][tex]A=\sqrt{9\times5\times3\times1}[/tex][tex]A=3\sqrt{15}\text{ }cm^2[/tex][tex]A=11.61\text{ }cm^2[/tex]Final Answer: Area of triangle is 11.61 sq cm.
