  In this paper, we prove an isoperimetric inequality for the triangular grid
graph which was conjectured by Adams, Gibson, and Pfaffinger, using the
compression technique of Bollob\'as and Leader. Moreover, we apply the
isoperimetric inequality to the Zero-Visibility Search game and Lions and
Contamination game in order to obtain lower bounds for the inspection number
and lion number respectively. We also provide searching strategies to prove
upper bounds for both the inspection number and lion number.
