Heron's Formula Problem

Heron's formula is

$S=\dfrac{a+b+c}{2}$

and the area is

$A=\sqrt{S(S-a)(S-b)(S-c)}$

With a triangle sides 2, 3, and 4, $S=\frac{2+3+4}{2}=4.5$ . When $S=4.5$ , the area would be

$A=\sqrt{4.5(4.5-2)(4.5-3)(4.5-4)}=\sqrt{4.5*2.5*1.5*0.5}=\sqrt{8.4375}\approx\large\color{#3D99F6}\boxed{2.9}$ .

Heron's formula states that with S being equal to half of the perimeter of the triangle, and A, B, and C being the 3 sides of the triangle. Plugging in the values, we get S = 4.5, and plugging it in, we get the area is root 8.4375( the root of {4.5 * 2.5 * 1.5 * 0.5}), which is around 2.9.