How do I find the area and perimeter of a square when all I'm given is a diaganol line cutting the square into two equal halves, with the length of the line being 6square root2, and the angles of the square are all 90 degrees, with the angle bisected by the line being 45 degrees on each side?

Question

How do I find the area and perimeter of a square when all I'm given is a diaganol line cutting the square into two equal halves, with the length of the line being 6square root2, and the angles of the square are all 90 degrees, with the angle bisected by the line being 45 degrees on each side?
My book was so very unclear and I really do not get it.'

Please help!

Marth · Answer

The diagonal divides the square into two special 45-45-90 right triangles. If you know the hypotenuse (given to you as 6 sqrt(2) ), can you find the length of a side? That side is also the length of the side of the square.