Question

Find the perimeter of the polygon defined by the coordinates (5, 12), (12,0), (0, 0), and (-4, 12). (Round to nearest tenth)

Answer 1

B) 47.5

1) Since a perimeter is the sum of all lengths side, we can use the distance formula between the four vertices to find out its perimeter:

A (5,12) , B (12,0) , C(0,0) and D(-4,12)

`\begin{gathered} d_{}=\sqrt[]{(x_2-x_1)^2+(y_2-y_(1))} \\ d_(AB)=\sqrt[]{(12_{}-5_{})^2+(0_{}-12)^2_{}}=\sqrt[]{193}\approx13.89 \\ d_(BC)=\sqrt[]{(0-12_{})^2+(0_{}-0)^2_{}}=12 \\ d_(CD)=\sqrt[]{(-4_{}-0_{})^2+(12-0)^2_{}}=4\sqrt[]{10}\approx12.65 \\ d_(DA)=\sqrt[]{(-4-5_{})^2+(12_{}-12)^2_{}}=9 \end{gathered}`

2) So, adding it all up we have the perimeter as

2p= 13.89 +12+12.65+9= 47.54

3) Hence, the answer is B) 47.5