Question

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.

Answer 1

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

Explanation:

`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"`