The slant height, l, is given as:
[tex]\begin{gathered} l=\sqrt[]{8^2+6^2} \\ l=\sqrt[]{64+36} \\ l=\sqrt[]{100} \\ l=10\text{ in} \end{gathered}[/tex]
The lateral area is given by the formula:
[tex]\begin{gathered} \text{Lateral Area= slant height }\times\frac{perimeter\text{ of base}}{2} \\ \text{Lateral Area= 10}\times\frac{6+6+6+6}{2} \\ \text{Lateral Area=10}\times\frac{24}{2} \\ \text{Lateral Area=}\frac{240}{2} \\ \text{Lateral Area = 120 in}^2 \end{gathered}[/tex]
The surface area of the pyramid is given by:
[tex]\begin{gathered} S\mathrm{}A_{pyramid}=\text{Area of the base + Lateral area} \\ S\mathrm{}A=\text{ (6}\times6)+120_{} \\ S.A=36+120 \\ S\mathrm{}A=156in^2 \end{gathered}[/tex]
The volume of the pyramid is given by:
[tex]\begin{gathered} V=\frac{1}{3}\times base\text{ area}\times height \\ V=\frac{1}{3}\times(6\times6)\times8 \\ V=\frac{1}{3}\times36\times8 \\ V=96in^3 \end{gathered}[/tex]
