Posted by **sam** on Wednesday, September 2, 2009 at 10:22pm.

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?

- Geometry -
**MathMate**, Wednesday, September 2, 2009 at 10:48pm
The diagonal (the slant of the triangle) of a square of side x is √2*x.

Can you figure the side using this relation?

- Geometry -
**Reiny**, Wednesday, September 2, 2009 at 10:51pm
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.

- Geometry -
**Reiny**, Wednesday, September 2, 2009 at 10:57pm
BTW, how did you come up with 8.5 for 4√2 ?

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