Geometry: What is the height of a solid pyramid So the question is OPQRS is a right pyramid whose base is a square of sides 12 cm each. Given that the the slant height of the pyramid is 15cm. And now I need to find the Height of the pyramid. 
I did my equation like this:
QR 1/2 = 6cm
HEIGHT^2 = 6^2+12^2
                   = 180
So height is root over 180 and thus I got 13.4 cm. But the answer at the back of my book says 13.7cm. Can anyone tell me what or why my answer is wrong?

Generalized formula, for any right pyramid having slant height $l$ & base as a regular n-gon with each side $a$, the normal height $h$ of the pyramid is given as follows
$$H=\frac{1}{2}\sqrt{4l^2-a^2cosec^2\frac{\pi}{n}}$$ 
Now,from the details of the problem, substituting slant height $l=15 cm\space$, each side of square base $a=12 cm$  & $n=4\space$ for a square base, we get normal height as follows
$$H=\frac{1}{2}\sqrt{4(15)^2-(12)^2cosec^2\frac{\pi}{4}}=\frac{1}{2}\sqrt{612}=\sqrt{153}\approx12.36931688 cm$$   
