The square shown below in figure 1 has side length 24 cm. it is divided into four
congruent quadrilaterals and rearranged to form the square in figure 2. the
square in the center of figure 2 has side length 10 cm. what is the side length of
the larger square in figure 2?

If the small square has side-length of 24 cm, then
its area is (24cm x 24cm) = 576 cm² .

So the area of all the shaded pieces is 576 cm², no matter
how they're cut up and jumbled around.  When they're moved
over and re-arranged to make the big square, the shaded part
is still 576 cm² .

The little white square in the center has side length of 10 cm,
so the area of that little square is (10cm x 10cm) = 100 cm².

Now, the total area of the big square is made up of 576 cm²
in the shaded parts, and 100 cm² in the white part.

Total area of the big square = (576cm² + 100cm²) = 676 cm² .

Since the big square is a square, its area is (side-length)² ,
and its side-length is  √(area) .

Side length =  √(676 cm²)  =  26 cm .