If the lateral surface area of a square-based pyramid with equal edges is $144\sqrt{3}$, what is the area of the base?

The lateral surface area of a square based pyramid having equal edges is $144√3$ cm^2. Find the area of base.

My Attempt: let,

length of base =$a$ slant height=$l$

Then,

$$L.S.A. of pyramid=144√3$$ $$2al=144√3$$ $$al=72√3$$.

Then, what should I do to go further.?

1 Answer

Write $T$ for the area of one of the 4 lateral triangles. Since every triangle is equilater we know that $$T=a\cdot a\sqrt 3/2\cdot 1/2=a^2\sqrt3 /4$$

We know that 4 triangles form the lateral area, thus: $$LSA=4T=a^2\sqrt 3$$

We need $a^2$ of course: $$a^2=LSA/\sqrt 3=144$$