Given that PQRS is a square with a side length of 28 cm. The points A, B, C, and D are the midpoints of the sides PQ, QR, RS, and SP respectively.

1. Calculate the area of the outer square PQRS: Area of square PQRS = side × side = 28 cm × 28 cm = 784 cm².

2. Determine the dimensions of the corner triangles: Since A, B, C, D are midpoints, they divide each side of the square PQRS into two equal halves. Therefore:

   • PA = AQ = QB = BR = RC = CS = SD = DP = 28 cm / 2 = 14 cm.

3. Calculate the area of one corner triangle: Consider the right-angled triangle formed at each corner, for example, triangle QAB. The legs of this triangle are AQ and QB.

   • Base (AQ) = 14 cm
   • Height (QB) = 14 cm Area of ΔQAB = (1/2) × base × height = (1/2) × 14 cm × 14 cm = (1/2) × 196 cm² = 98 cm².

4. Calculate the total area of the four corner triangles: There are four such congruent triangles (ΔQAB, ΔRBC, ΔSCD, ΔPDA). Total area of 4 triangles = 4 × 98 cm² = 392 cm².

5. Calculate the area of the inner square ABCD: The area of the inner square ABCD can be found by subtracting the total area of the four corner triangles from the area of the outer square PQRS. Area of square ABCD = Area of square PQRS - Total area of 4 triangles Area of square ABCD = 784 cm² - 392 cm² = 392 cm².

Alternatively, we could find the side length of square ABCD using the Pythagorean theorem for one of the triangles, e.g., ΔQAB: AB² = AQ² + QB² = 14² + 14² = 196 + 196 = 392. Since ABCD is a square, its area is AB². Area of square ABCD = 392 cm².