Question

What is the lateral area of the rectangular pyramid whose net is shown

Answer 1

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:

`\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}`

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:

`\begin{gathered} A=(b\cdot L)/(2)=(25\cdot31.58)/(2)=(789.5)/(2)=394.75 \\ A=394.75in^2 \end{gathered}`

therefore, the lateral area of the rectangular pyramid is 394.75 in^2