Question

1. what is the perimeter of the given composite figure? (round your answer to the nearest tenth.)

Explanation:

Step1: Identify side - lengths

Count the grid - squares for straight sides. For the slanted side, use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Calculate lengths of straight sides

The vertical side on the left from $( - 12,-12)$ to $( - 12,18)$ has length $|18-( - 12)|=30$. The horizontal side at the bottom from $( - 12,-12)$ to $(6,-12)$ has length $|6-( - 12)| = 18$. The vertical side from $(6,-12)$ to $(6,0)$ has length $|0-( - 12)| = 12$. The horizontal side from $(6,0)$ to $(12,0)$ has length $|12 - 6|=6$.

Step3: Calculate length of slanted side

Let the two points of the slanted side be $(12,0)$ and $(18,12)$. Using the distance formula $d=\sqrt{(18 - 12)^2+(12 - 0)^2}=\sqrt{6^2+12^2}=\sqrt{36 + 144}=\sqrt{180}=6\sqrt{5}\approx13.4$. The horizontal side from $(18,12)$ to $( - 12,12)$ has length $| - 12-18| = 30$.

Step4: Sum up all side - lengths

$P=30 + 18+12 + 6+13.4+30=109.4$.

Answer:

$109.4$