Answer :
A square pyramid has 5 faces. A base square and 4 triangles. The total surface area is a sum of the area of the individual faces.
[tex]\begin{gathered} \text{Area of base square = l}^2\text{ where } \\ l=\text{ length of side = }16 \\ \text{Therefore area = 16}^2\text{ = 256 sq units} \end{gathered}[/tex][tex]\begin{gathered} \text{Area of traingle = }\frac{1}{2}\text{ }\times base\text{ }\times perpendicular\text{ height} \\ \text{where base = }10 \\ \text{Perpendicular height will be obtained from pythagoras theorem } \\ Opp\text{= }\sqrt[]{hyp^2-\text{adj}} \\ \text{= }\sqrt[]{10^2-8^2}=6 \\ \end{gathered}[/tex]We now have to find the area of the other 4 faces and sum it all
[tex]\text{Area of the 4 triangles =4( }\frac{1}{2}\times16\text{ }\times\text{ 6) = 192 sq units }[/tex]Total surface area of the pyramid = area of base square + area of 4 triangles
[tex]=\text{ 192 +256 = 448 sq units}[/tex]