The given diagram is a pentagon with different side measurements.
The perimeter is defined as the sum of all external boundaries of the figure.
So the perimeter (P) of the pentagon is equal to the sum of the 5 sides of the figure,
[tex]\begin{gathered} P=(3t^2-9)+(3t^2-9)+(2t^2+5)+(2t^2+5)+(t^3-t^2+8) \\ P=3t^2-9+3t^2-9+2t^2+5+2t^2+5+t^3-t^2+8 \\ P=t^3+(3t^2+3t^2+2t^2+2t^2-t^2)+(-9-9+5+5+8) \\ P=t^3+9t^2+(0) \\ P=t^3+9t^2 \end{gathered}[/tex]
Thus, the perimeter of the figure is,
[tex]t^3+9t^2[/tex]
