From the given values for the two side of triangles in the side of the present pyramid, we can do as follows:
We are going to use the Pythagorean theorem to find the height of this triangle.
[tex]\begin{gathered} h^2+7^2=25^2 \\ h^2=625-49=576 \\ h=24 \end{gathered}[/tex]
Now, we can use the values for the base and height of the triangle that is one of the sides of the pyramid to calculate its area:
[tex]\begin{gathered} A_{\text{triangle}}=\frac{b\times h}{2} \\ A_{\text{triangle}}=\frac{24\times14}{2}=168 \end{gathered}[/tex]
And because the pyramid has 8 sides with the same geometry and size, all we need now is multiply this value by 8.
[tex]\begin{gathered} A_{\text{lateral}}=8\times A_{triangle} \\ A_{\text{lateral}}=8\times168 \\ A_{\text{lateral}}=1,344 \end{gathered}[/tex]
From this, we can say that the answer is 1,344
