A circle inscribed in a square has a diameter of 14
cm. If a smaller square is inscribed within this circle, calculate the area of the smaller square. Also, find the area of the region between the two squares.

The diameter of the circle is 14 cm, so its radius is 7 cm.  The diagonal of the smaller square is equal to the diameter of the circle, which is 14 cm. Using the formula for the diagonal of a square (d = a√2),  where a is the side of the square, we find that the side of the smaller square is a = 14/√2 = 7√2. Area of smaller square = (7√2)² = 98 cm². Area of larger square = 14² = 196 cm². Area of the region = 196 - 98 = 98 cm². Correct answer: a) Area of smaller square = 98 cm², Area of region = 98 cm²