Given the information on the picture, we have the following rectangular pyramid:
Notice that we get the following right triangle:
then we can use the pythagorean theorem to find the missing length:
[tex]\begin{gathered} L^2=(29)^2+(12.5)^2 \\ \Rightarrow L^2=841+156.25=997.25 \\ \Rightarrow L=\sqrt[]{997.25}=31.58 \\ L=31.58in \end{gathered}[/tex]
Now we have the base and the height of a lateral side:
Then, using the formula for the area of a triangle, we get the following:
[tex]\begin{gathered} A=\frac{b\cdot L}{2}=\frac{25\cdot31.58}{2}=\frac{789.5}{2}=394.75 \\ A=394.75in^2 \end{gathered}[/tex]
therefore, the lateral area of the rectangular pyramid is 394.75 in^2
