Geometry
posted by sam on .
How do I figure out the area and perimeter of a square if all I know is the cross (top left corner to bottom right corner) measurement? I have a square with the cross measurement of 8.5 (or 4 X sq root of 2, i rounded to 8.5). The square looks like it is cut in half to look like 2 triangles and in the corner of one triangle it says 45 degrees.
Please help me, I am so confused, is there a formula to figure this problem out?

The diagonal (the slant of the triangle) of a square of side x is √2*x.
Can you figure the side using this relation? 
I don't know what grade level you are in, but since you seem to know about square roots, I am somewhat surprised that you don't know the Pythagorean Theorem.
Since you are dealing with a square, let each side of the square be x
then x^2 + x^2 = (4√2)^2
2x^2 = 32
x^2 = 16
x = 4
Now that we know that we have a 4 x 4 square, we can easily find its area and perimeter. 
BTW, how did you come up with 8.5 for 4√2 ?