Question

what is the perimeter of the composite figure? round to the nearest tenth

Explanation:

Step1: Identify horizontal and vertical side - lengths

Count the grid - squares for horizontal and vertical sides.
The left - hand vertical side from $( - 12,-12)$ to $( - 12,18)$ has length $18-( - 12)=30$.
The bottom - hand horizontal side from $( - 12,-12)$ to $(6,-12)$ has length $6-( - 12)=18$.
The right - hand vertical side from $(6,-12)$ to $(6,3)$ has length $3-( - 12)=15$.
The horizontal side from $(6,3)$ to $(18,3)$ has length $18 - 6=12$.
The diagonal side from $(18,3)$ to $(24,18)$:
Use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 18,y_1 = 3,x_2 = 24,y_2 = 18$.
$d=\sqrt{(24 - 18)^2+(18 - 3)^2}=\sqrt{6^2+15^2}=\sqrt{36 + 225}=\sqrt{261}\approx16.2$.

Step2: Calculate the perimeter

Add up all the side - lengths.
$P=30 + 18+15 + 12+16.2=91.2$.

Answer:

$91.2$