Question 563718
A square is equal on all 4 sides.


Let each side = x.


The diagonal and two sides form a right triangle.


We can use the Paythagorean Theorem to start with.


x^2 + x^2 = 16^2


2x^2 = 256


x^2 = 256/2


x^2 = 128


Take square root of both sides.


sqrt{x^2} = sqrt{128}^2


x = sqrt{64} * sqrt{2}


x = 8(sqrt{2})


Now that we know the value for x, we use A = (side)^2 to find the area.


A = [8(sqrt{2})]^2


A = 128m^2