If the square has been plotted in a graph, you can go about finding the diagonal of it by measuring the midpoint.
(1) Find the coordinates of the vertices of the square
(2) Use the coordinates of two vertices that are across from each other. Plug them into the midpoint equation: (X1 + X2)/2 , (Y1 + Y2)/2, and use your answers as the coordinates of the midpoint (x,y)
(3) Draw a straight line crossing through the midpoint from one opposite vertex to another. That is your diagonal.
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Use Pythagoras on the triangle formed by two adjacent sides and the diagonal between their other ends: diagonal = √(122 + 122) = 12 x √2 ~= 16.97 units
A 30x30 Square A square has 4 equal sides, and when we add up the four sides we get 120. So to find the the square, we can do 120/4 = 30 This tells us that the square is 30x30
If the length of a side of the square is S units then the diagonal is S*sqrt(2) units in length.
They came from geometry. If you have a square whose sides are 1 unit long then its diagonal is sqrt(2) units long.
The diagonal is 33.941 units.