Given,

In a triangular based prism,

PQ ⊥ RQ, PQ = 8 cm, QR = 6 cm and RR' = 15 cm

To find:

Lateral surface area of the prism (LSA)

Here, In the right angled triangle PQR,

PR = \(\sqrt{PQ^2+QR^2}\)

= \(\sqrt{8^2+6^2}\)

= \(\sqrt{64+36}\)

= \(\sqrt{100}\)

= 10 cm

**∴ Perimeter of the triangular base = PQ + QR + PR = 8 cm + 6 cm + 10 cm = 24 cm**

Now, by formula

Lateral surface area of the prism (LSA) = perimeter of base x height

= 24 cm x 15 cm

= 360 cm^{2} is the required answer.