 # Which expression can be subtracted from the area of the rectangle to find the area of parallelogram rstu? 2 (18 4) one-half (18 4) (18 4) (18 - 4)

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149 cents The expression can be subtracted from the area of the rectangle to give the area of the parallelogram RSTU (18+4).

### What is the area of the rectangle?

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).  