[tex]253.30\:yd²[/tex]
1) In this triangular pyramid, we can see that there are some measurements. Let's enlist them:
Slant height: 14.866 yd
Height=14
height of the base: 8.66
length of the base side: 10 yd
2) So, let's find the area of that pyramid:
[tex]\begin{gathered} Base\:Area=\frac{a^2\sqrt{3}}{4}=\frac{10^2\sqrt{3}}{4}=25\sqrt{3} \\ Lateral\:Area=3\times(\frac{10\times14}{2})\Rightarrow210 \\ TSA=210+25\sqrt{3}\approx253.30\:yd² \end{gathered}[/tex]
Note that we have used the base times height time 1/2 for the3 lateral triangle area the base triangle is an equilateral one.
