The expression can be subtracted from the area of the rectangle to give the area of the parallelogram RSTU (18+4).
The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
The coordinates of parallelogram RSTU are
R(-4, -3), S(-5, 1), T(4, 3), U(5, -1)
The lengths of the sides are
RS = 4.1231
RT = 10
ST = 9.2195
SU = 10.198
TU = 4.1231
UR = 9.2195
Therefore, by definition of a parallelogram, we have;
RS║TU and ST║UR
The slope of RS = (1 - (-3))/(-5 - (-4)) = -4
The slope of ST = (3 - 1)/(4 - (-5)) = 2/9
The equation of the line perpendicular to ST is
y - 1 = -9/2×(x - (-5))
y = -9x/2 - 43/2
The equation of RS = y - (-3) = 1/4×(x - (-4)) = x/4 + 1
y = x/4 - 2
The point where the two lines meet
-9x/2 - 43/2 = x/4 - 2
x = -78/19
y = -115/38
The length of the side of the rectangle = 4.1245
The excess width of the rectangle = 0.1085
The expression can be subtracted from the area of the rectangle to give the area of the parallelogram RSTU (18+4).
Learn more about the area:
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