Each leg of an isosceles right triangle is sqrt(2)/2 of the hypotenuse.
The area of the figure is therefore the product of the legs divided by 2, namely
Area = 24*sqrt(2)/2 * 24*sqrt(2)/2 ÷ 2
=24² (sqrt(2))² /(2*2*2)
= 576 * 2 / (8)
= 144 sq. ft.