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) .
