The slant height is 51 cm. The radius can be found from the Pythagorean theorem:
r^2 + (24 cm)^2 = (51 cm)^2
r^2 = (51^2 -24^2) cm^2 = 2025 cm^2
r = 45 cm
The area of the circular base is
A = π·r^2 = 2025π cm^2
The lateral area is
A = πrs . . . . . where s is the slant height
A = π·(45 cm)·(51 cm) = 2295π cm^2
Then the total area is
total area = base area + lateral area
= 2025π cm^2 + 2295π cm^2
= 4320π cm^2