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Lato $lo= x$;

base $b= x-6$;

perimetro:

$x-6+2x = 72$

$3x = 72+6$

$3x = 78$

$x= \frac{78}{3}$

$x= 26$

per cui:

lato $lo= x = 26~cm$;

base $b= x-6 = 26-6 = 20~cm$;

altezza $h= \sqrt{lo^2-\big(\frac{b}{2}\big)^2} = \sqrt{26^2-\big(\frac{20}{2}\big)^2} = \sqrt{26^2-10^2} = 24~cm$ (teorema di Pitagora);

area $A= \dfrac{b·h}{2} = \dfrac{20×24}{2} = 240~cm^2$.