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?

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 **.

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