Question

The area of the trapezoid shown below is equal to 270 square units. Find its perimeter and round your answer to the nearest unit.

Answer 1

$Let\: h \:be \:the \:height\: of \:the \:trapezoid.$

$area \: = \frac{1}{2} × h × (10 + 10 + 3 + 4) = 270$

$h \:= \:20 : solve \:for \:h$

${20}^{2}+ {3}^{2} = {L}^{2}: \:Pythagora’s \:theorem \:applied \:to \:the \:right \:triangle \:on \:the\: left$

$L\: = \: sqrt(409)$

${20}^{2}+ {4}^{2}= {R}^{2}: \: Pythagora's \:theorem \:applied\: to\:the \:right \:triangle\: on \:the \:right$

$R \: = \:sqrt(416)$

$perimeter \:= \:sqrt(409) + 10 + sqrt(416) + 17 = 27 + sqrt(409) + sqrt(416)$