The base of a pyramid is a regular polygon, whose total surface area is 340 sq. cm and area of base is 100sq. cm. If area of each lateral surface is 30 sq. cm, then find the number of lateral surfaces of the pyramid.

8

T.S.A. of pyramid = lateral surface area + area of  base

⇒ 340 = n × area of 1 face + 100

n = number of faces

⇒ 340 - 100 = n × 30

⇒ \(\frac{240}{30}\) = n

n = 8