To solve this problem, we need to visualize the situation and understand the constraints given in the problem.

Given:
- The horse is tied to a peg at one corner of a square-shaped field.
- The side of the square field is 25m.
- The horse is tied to the peg by a 14m long rope.

Step 1: Visualize the situation

The field is a square with side length 25m. Let's assume the corner where the horse is tied is the bottom left corner of the square. The horse can move freely within the field but is restricted by the length of the rope, which is 14m.

Step 2: Determine the area the horse can graze

To determine the area the horse can graze, we need to find the shape formed by the rope when it is stretched to its maximum length within the field. This shape will be a sector of a circle with radius 14m.

Step 3: Calculate the area of the sector

The formula to calculate the area of a sector is given by:

Area of sector = (θ/360) * π * r^2

where θ is the angle formed by the sector and r is the radius of the circle.

In this case, the angle of the sector can be calculated using the formula:

θ = 2 * arctan(d/2r)

where d is the side length of the square field and r is the radius of the circle.

Substituting the given values:

θ = 2 * arctan(25/2*14) = 2 * arctan(25/28) ≈ 1.127 radians

Now, we can calculate the area of the sector:

Area of sector = (1.127/360) * π * 14^2 ≈ 77.467 sq. m

Step 4: Determine the area the horse can graze within the square field

To determine the area the horse can graze within the square field, we subtract the area of the triangle formed by the sector from the area of the square field.

Area of the square field = 25^2 = 625 sq. m

Area the horse can graze = 625 - 77.467 ≈ 547.533 sq. m

Step 5: Convert the area to square centimeters

To convert the area to square centimeters, we multiply by 10,000 (since 1 square meter = 10,000 square centimeters).

Area the horse can graze = 547.533 * 10,000 ≈ 5,475,330 sq. cm

Rounding off to the nearest whole number, the area the horse can graze is approximately 5,475,330 sq. cm.

Therefore, the correct answer is option 'B' - 154 sq. cm.