Draw the right angles on the rotated square. 2B is actually a quadrant. Each semicircle is 4B. Step 1: find area of half a square. Step 2: find the area of semicircle (also 4B). Step 3: find area of triangle (also half a square). There are 4 shaded parts in total. To find 2 of them, take area of half a square - area of triangle - 2B. To get all 4 parts, multiply previous result by 2.

Notice the shaded areas are equal to the unshaded areas. You can fit them into one side of the square.
The shaded area is just half a square minus a semicircle.
(6cm x 12cm) - (π x 6cm x 6cm x ½)
= 72cm² - 56.5486678cm²
= 15.4513322cm²
≈ 15.45cm² (2 decimal places)