Question

what is the perimeter of the trapezoid with vertics q(8,8) R(14,16) S(20,16) and T(22,8) roung to the nearest hundrenths if necessary

Answer 1

`~\hfill \stackrel{\textit{\large distance between 2 points}}{d = √(( x_2- x_1)^2 + ( y_2- y_1)^2)}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ Q(\stackrel{x_1}{8}~,~\stackrel{y_1}{8})\qquad R(\stackrel{x_2}{14}~,~\stackrel{y_2}{16}) ~\hfill QR=√([ 14- 8]^2 + [ 16- 8]^2) \\\\\\ QR=√(6^2+8^2)\implies QR=10 \\\\[-0.35em] ~\dotfill`

`R(\stackrel{x_1}{14}~,~\stackrel{y_1}{16})\qquad S(\stackrel{x_2}{20}~,~\stackrel{y_2}{16}) ~\hfill RS=√([ 20- 14]^2 + [ 16- 16]^2) \\\\\\ RS=√(6^2)\implies RS=6 \\\\[-0.35em] ~\dotfill\\\\ S(\stackrel{x_1}{20}~,~\stackrel{y_1}{16})\qquad T(\stackrel{x_2}{22}~,~\stackrel{y_2}{8}) ~\hfill ST=√([ 22- 20]^2 + [ 8- 16]^2) \\\\\\ ST=√(2^2+(-8)^2)\implies ST=√(68) \\\\[-0.35em] ~\dotfill`
`T(\stackrel{x_1}{22}~,~\stackrel{y_1}{8})\qquad Q(\stackrel{x_2}{8}~,~\stackrel{y_2}{8}) ~\hfill TQ=√([ 8- 22]^2 + [ 8- 8]^2) \\\\\\ TQ=√((-14)^2)\implies TQ=14 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{\large Perimeter}}{10~~ + ~~6~~ + ~~√(68)~~ + ~~14~~} \approx ~~ 38.25`