Answer:
7.07106781187 square units
Explanation:
5×√2=7.07106781187
If you can imagine bisecting the smaller square you will notice the length of the diagonal line is equal to the side of the larger square; also the new triangles created by drawing a line between the opposite vertices of a perfect square, creates two congruent right triangles; with angles 45 45 and 90.
By reworking Pythagorean theorem we find the length of the hypotenuse.
As we noticed before, the diagonal of a square divides the square into two congruent right triangles.
Legs are square sides and the length of diagonal of the square is the hypotenuse. Given the side length of the square:
a² + a² = diagonal²
diagonal = √(a² + a²) = √(2 * a²) which simplifies to
diagonal = a√2
