Let the length of the sides of triangle be 2x, 3x and 4x.

Perimeter of triangle = 180cm

⇒ $2x+3x+4x=180$

⇒ $9x=180$

⇒ $x=\frac{180}{9}$ = 20cm

Then the sides of the triangle are:

$2x=2\times 20=40cm;3x=3\times 20$ = 60cm and $4x$ = 4$\times 20$= 80cm

Using Heron's formula

Area of triangle = $\sqrt{s}(s-a)(s-b)(s-c)$

Where s = $\frac{a+b+c}{2}$

Let a = 40cm, b = 60cm, c = 80cm and s = $\frac{40+60+80}{2}=\frac{180}{2}$ = 90cm

⇒ A = $\sqrt{9}0(90-40)(90-60)(90-80)=\sqrt{9}0\times 50\times 30\times 10=\sqrt{1}350000$

∴ A =1162cm${}^2$ (to the nearest cm${}^2)$