A trapezoid has an area of #160# #cm^2#. The length of one base is #20# #cm# and the height is #10# #cm#. What is the length of the other base?

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Answer 1 · 2018-05-14T14:18:13

#12 \ "cm"#

Area of a trapezoid is given by:

#A=(b_1+b_2)/2*h#

where:

#b_1,b_2# are the two bases of the trapezoid

#h# is the height of the trapezoid

So here, we have:

#160 \ "cm"^2=(20 \ "cm"+b_2)/2*10 \ "cm"#

#320 \ "cm"^2=10 \ "cm"(20 \ "cm"+b_2)#

#20 \ "cm"+b_2=(320color(red)cancelcolor(black)"cm"^2)/(10color(red)cancelcolor(black)"cm")=32 \ "cm"#

#:.b_2=32 \ "cm"-20 \ "cm"#

#=12 \ "cm"#