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  3. Mathematics
  4. The base of a pyramid is an n-sided regular polygon of area 360 cm 2. The total surface area of the pyramid is 900 cm 2. Each lateral face of the pyramid has an area of 30 cm 2. Find n.

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Q. The base of a pyramid is an $n$-sided regular polygon of area $360\, cm ^2$. The total surface area of the pyramid is $900 \,cm ^2$. Each lateral face of the pyramid has an area of $30 cm ^2$. Find $n$.

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Solution:

Total area of the lateral faces $=900-360=540 \,cm ^2$.
Number of lateral faces it has $\frac{540}{30}=18$.