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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?

Answer 1

Sadie Adams

#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"#

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Answer 2

Savannah Aguilar

Using the formula for the area of a trapezoid:

Area = (1/2) * (sum of the lengths of the bases) * height

We can rearrange the formula to solve for the length of the other base:

Other base = (2 * Area / height) - given base length

Plugging in the given values:

Other base = (2 * 160 cm^2 / 10 cm) - 20 cm

Other base = (320 cm / 10 cm) - 20 cm

Other base = 32 cm - 20 cm

Other base = 12 cm

Therefore, the length of the other base is 12 cm.

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