Question

In the image below, there are two large congruent* squares with sides 7 units long and four small

congruent* squares with sides 3 units long. If the shaded figure is also a square, what is its area in square
units?
"Congruent means identical in shape and size.
7
3

Answer 1

The area of the shaded square is 64 square units as the shaded figure in the image is a square.

We notice that the shaded square is formed by combining the leftover parts of the two large squares after removing the four small squares. Each leftover part has a width of 7 units (the side length of the large squares) minus 3 units the side length of the small squares on each side.

Therefore, each leftover part has a width of 4 units and the shaded square is formed by combining two of these leftover parts, its side length is 2 * 4 units = 8 units.

The area of a square is calculated by squaring its side length. The area of the shaded square is 8 units * 8 units = 64 square units.