ANSWER
• Lateral surface area: ,73 cm²
,• Total surface area: ,93 cm²
EXPLANATION
The lateral surface area is the sum of the areas of the triangles. There are two triangles with dimensions: base = 4cm, height = 8cm and two triangles with dimensions: base = 5cm, height = 8.2cm.
The lateral surface area LSA is:
[tex]\begin{gathered} \text{LSA}=2\cdot(\frac{4\cdot8}{2})+2\cdot(\frac{5\cdot8.2}{2}) \\ \text{LSA}=4\cdot8+5\cdot8.2 \\ \text{LSA}=73\operatorname{cm}^2 \end{gathered}[/tex]The total surface area SA is the LSA plus the area of the base of the pyramid, which is a rectangle with dimensions: 4cm x 5cm:
[tex]\begin{gathered} SA=\text{LSA}+4\cdot5 \\ SA=73\operatorname{cm}+20\operatorname{cm}^2 \\ SA=93\operatorname{cm}^2 \end{gathered}[/tex]
