Question

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

Explanation:

Step1: Identify lengths of straight - line segments

Count the grid units for horizontal and vertical segments.
Left - hand vertical segment: From $y = 18$ to $y=-12$, length is $18 - (-12)=30$.
Bottom - hand horizontal segment: From $x=-12$ to $x = 6$, length is $6-(-12)=18$.
Right - hand vertical segment from $y = 3$ to $y = 18$ (assuming the start of the slanted line is at $y = 3$ and end at $y = 18$), length is $18 - 3=15$.
Small horizontal segment from $x = 6$ to $x = 15$ (assuming end - point of small horizontal part), length is $15 - 6 = 9$.

Step2: Calculate length of slanted segment

Use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Let the two endpoints of the slanted segment be $(x_1,y_1)=(15,3)$ and $(x_2,y_2)=(21,18)$. Then $d=\sqrt{(21 - 15)^2+(18 - 3)^2}=\sqrt{6^2+15^2}=\sqrt{36 + 225}=\sqrt{261}\approx16.2$.

Step3: Sum up all lengths

Perimeter $P=30 + 18+15 + 9+16.2=88.2$.

Answer:

$88.2$