The base triangle has sides 5, 12, 13 — this is a right triangle (since \(5^2 + 12^2 = 25 + 144 = 169 = 13^2\).

Base area = \(\dfrac{1}{2} \times 5 \times 12 = 30\ \text{cm}^2\

Perimeter of base = \(5 + 12 + 13 = 30\ \text{cm}\

Lateral surface area = Perimeter × Height = \(30 \times 10 = 300\ \text{cm}^2\

Total SA = Lateral SA + 2 × Base area = \(300 + 2 \times 30 = 300 + 60 = 360\ \text{cm}^2\

Wait — checking options: 360 is option A. Let me recheck — actually answer is A (360). Note: This is correctly 360.