This figure is made up of a rectangle and parallelogram. What is the area of this figure? Enter your answer in the box. Do not round any side lengths.

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Answer 1 · 2018-04-09T05:17:32

#color(green)("Total Area of the given figure " = color(brown)(51 color(green)(" sq units"#

#To find Area of Parallelogram ABCF & Rectangle CDEF"#

#"Coordinates of " A(4,-9), B(7,-7)C (-3, 7), D (6,1), E (4,-2), F (-5,4), G(4,-7)#

#"Area of parallelogram ABCF = BC * BG = 4 * 3 = 12#

#bar(CD) = bar(EF) = sqrt((-3-6)^2 + (7-1)^2) = sqrt(117)#

#bar(CF) = bar(DE) = sqrt((-3+5)^2 + (7-4)^2) = sqrt(13)#

#"Area of Rectangle " CDEF = CD * DE = sqrt117 * sqrt13 = 39#

#"Total Area of the figure " ABCDEF = 12 + 39 = 51 "sq units"#