A triangular prism has a base formed by a triangle

Solution:

The base of the prism is a triangle with sides 9 cm, 12 cm, and 15 cm.
This is a right-angled triangle because $9^2 + 12^2 = 15^2$.

So, its sides act as the perimeter for lateral surface area.

Lateral surface area of a prism
= Perimeter of base × height

Perimeter of triangle
$= 9 + 12 + 15 = 36$ cm

Height of prism = 10 cm

Lateral surface area
$= 36 \times 10 = 360$ cm²

Answer: The lateral surface area is $360 \text{ cm}^2$.