Question

to find the area of parallelogram rstu, juan starts by drawing a rectangle around it. each vertex of parallelogram rstu is on a side of the rectangle he draws. which expression can be subtracted from the area of the rectangle to find the area of parallelogram rstu? 2 (18 + 4) $\frac{1}{2}$ (18 + 4) (18 + 4) (18 - 4)

Explanation:

Step1: Analyze the method

When finding the area of a parallelogram by enclosing it in a rectangle, the difference between the area of the rectangle and the sum of the areas of the two pairs of congruent right - triangles outside the parallelogram gives the area of the parallelogram. The two pairs of right - triangles together form two congruent rectangles.

Step2: Consider the areas of the extra parts

The two pairs of right - triangles that need to be removed from the area of the rectangle have a combined area that is equivalent to the area of two rectangles with dimensions related to the "over - hanging" parts of the rectangle around the parallelogram. The sum of the areas of these two pairs of right - triangles is equivalent to the area of a rectangle with dimensions such that the expression for the area to be subtracted is \(2(18 + 4)\) (assuming the relevant side - length related values are 18 and 4).

Answer:

\(2(18 + 4)\)