Question

Find the perimeter of the polygon defined by the coordinates (5, 8), (12, 0), (-5, 0), and (-12, 8). (Round to nearest tenth)

A)53.2
B)55.3
C)56.3
D)57.3

Answer 1

`\displaystyle\\\text{We have the points:}\\E(5,~8)\\F(12,~0)\\G(-5,~0)\\H(-12,~8)\\\\EF=√((5-12)^2+(8-0)^2)=√((-7)^2+8^2)=\\=√(49+64)=√(113)\approx\boxed{\bf10.63}\\\\FG=12-(-5)=12+5=\boxed{\bf17}\\\\GH=√((-5-(-12))^2+(0-8)^2)=√(7^2+(-8)^2)=\\=√(49+64)=√(113)\approx\boxed{\bf10.63}\\\\HE=|-12-5|=|-17|=\boxed{\bf17}\\\\P=EF+FG+GH+HE=10.63+17+10.63+17=55.26\approx\boxed{\bf55.3}\\\\\text{Correct answer: }~B)`