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

Question

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.?

Please give your questions informative titles. "LSA of pyramid" is neither informative nor a question. — symplectomorphic, Dec 25 '16 at 05:35

score 1 · Accepted Answer · answered Dec 25 '16 at 06:29

1

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: $$a^2=LSA/\sqrt 3=144$$

answered Dec 25 '16 at 06:29

Maffred

4,016

Hello, How is every triangle equilateral? – pi-π Dec 25 '16 at 11:06
Because the pyramid has equal edges. – Maffred Dec 26 '16 at 00:24

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

1 Answers1