How do you find the area of the parallelogram with vertices (4,5), (9, 9), (13, 10), and (18, 14)?

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Answer 1 · 2015-02-23T13:09:58

Calculate the areas of the four trapezoids formed by the line segments, the X-axis, and the line segments joining the given vertices to the X-axis.

Subtract the lower two trapezoid areas from the upper two.

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General form of Trapezoid Area = #Delta x + ave_y#

#A1 = (9 - 4) xx ( (9+5)/2)#
#= 5 xx 7 = 35#

#A2 = (18 - 9) xx ((9+14)/2)#
# = 9 xx 11 1/2 = 103 1/2#

#B1 = (13 - 4) xx ((5+10)/2)#
#= 9 xx 7 1/2 = 67 1/2#

#B2 = (18 -13) xx ((14 + 10)/2)#
# = 5 xx 12 = 60#

Area of parallelogram
#= (A1 + A2) - (B1 + B2)#
#= (35 + 103 1/2) - (67 1/2 + 60)#
#= 138 1/2 - 127 1/2#
#= 11#

(always assuming my basic arithmetic is correct).