To find the area of the least-sized square that can be inscribed in a given square, we need to understand the properties of squares and their inscribed squares.

Properties of a Square:
1. All sides of a square are equal.
2. Opposite sides of a square are parallel.
3. All angles of a square are right angles (90 degrees).

Inscribed Square:
An inscribed square is a square that is drawn inside another shape in such a way that all four vertices of the square lie on the sides of the outer shape.

To find the area of the inscribed square, we can use the following steps:

Step 1: Draw the given square ABCD with side length 10 cm.
Step 2: Divide each side of the square into two equal parts. This will give us four smaller squares.
Step 3: Connect the midpoints of opposite sides of the larger square to form a smaller square inside it.

Now, let's calculate the area of the inscribed square.

Step 1: Draw the given square ABCD with side length 10 cm.

ABCD is a square with side length 10 cm.
[IMAGE: Square ABCD with side length 10 cm]

Step 2: Divide each side of the square into two equal parts. This will give us four smaller squares.

Divide each side of ABCD into two equal parts.
[IMAGE: Square ABCD divided into four smaller squares]

Step 3: Connect the midpoints of opposite sides of the larger square to form a smaller square inside it.

Connect the midpoints of AB, BC, CD, and DA to form a smaller square EFGH inside ABCD.
[IMAGE: Inscribe a square EFGH inside ABCD]

Now, we can see that the side length of the inscribed square EFGH is half the side length of ABCD. Therefore, the side length of EFGH is 5 cm.

The area of a square is given by the formula: Area = side length * side length.

So, the area of the inscribed square EFGH = 5 cm * 5 cm = 25 cm^2.

Therefore, the correct answer is option (b) 25 cm^2.