Question

Find the slant height of a square based right pyramid whose perimeter of the base is $40$m and its lateral surface area is $120m^2$. What is its total surface area?

Answer 1

Given: $P=4a=40m,$ L.S.A$=120m^2$, we have to find l and T.S.A. Using L.S.A$=\frac{1}{2}Pl$, we have $120=\frac{1}{2}\times 40\times l$.
This gives $l=6$m. Thus, slant height$=6$m.
We also have $40=P=4a$ so that $a=10$. Hence $B=a^2=100m^2$. This gives T.S.A$=B+L.S.A=100+120=220m^2$.