The base of triangle is equal to the perimeter of a square whose diagonal is 9$\sqrt{2}$ cm, and its height is equal to the side of a square whose area is 144$cm^{2}$. The area of the triangle (in $cm^{2}$) is: 

216

We know that,

Diagonal of square = Side\(\sqrt {2}\)

Area of triangle = \(\frac{1}{2}\) × base × height 

Perimeter of square = 4 × side 

Side \(\sqrt {2}\)= 9\(\sqrt {2}\)

Side = 9

Perimeter = 4 × 9 = 36

24 = base of triangle according to question

Now height is equal to side of square whose area is 144cm² 

Height² = 144

Height = 12

Height of the triangle is equal to side of square = Area of triangle =\(\frac{1}{2}\) × 12× 36 = 216