(a) The perimeter of the cross-section RASB is the sum of the arc lengths ARB and RBS. The arc length ARB is given by \(2.5 \times \frac{4\pi}{3}\) and the arc length RBS is given by \(2.24 \times \frac{5\pi}{6}\). Therefore, the perimeter is:

\(2.5 \times \frac{4\pi}{3} + 2.24 \times \frac{5\pi}{6} = 10.47 + 5.86 = 16.34\)

(b) The area of triangle AOB is \(\frac{1}{2} \times 2.5^2 \times \sin \frac{2\pi}{3} = 2.706\) and the area of triangle APB is \(\frac{1}{2} \times 2.24^2 \times \sin \frac{5\pi}{6} = 1.254\). The difference in area is:

\(2.706 - 1.254 = 1.45\)

(c) The area of the cross-section RASB is the sum of the areas of sectors OARB and PASB plus the area of quadrilateral OAPB. The area of sector OARB is \(\frac{1}{2} \times 2.5^2 \times \frac{4\pi}{3} = 13.09\) and the area of sector PASB is \(\frac{1}{2} \times 2.24^2 \times \frac{5\pi}{6} = 6.57\). Adding the difference in area from part (b), the total area is:

\(13.09 + 6.57 + 1.45 = 21.1\)