Question

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) (18 - 4) (18 + 4) 1(18 - 4)

Explanation:

Step1: Understand the method

To find the area of a parallelogram by enclosing it in a rectangle, we subtract the combined area of the extra right - angled triangles formed around the parallelogram. When we enclose a parallelogram in a rectangle, the extra parts are two congruent right - angled triangles.

Step2: Analyze the areas of the triangles

Let's assume the base and height of the parallelogram are related to the dimensions of the rectangle. If we consider the fact that the two congruent right - angled triangles together have an area that can be calculated based on the differences in the side - lengths of the rectangle and the parallelogram. In this case, the two congruent right - angled triangles' combined area is equivalent to the area of a rectangle with dimensions that are related to the "extra" lengths outside the parallelogram. If we assume the relevant lengths are such that the combined area of the two triangles is \(2\times\frac{1}{2}\times( \text{base}\times\text{height of the triangle})\). If we consider the lengths in terms of the rectangle's dimensions, the combined area of the two triangles (the part to be subtracted from the rectangle's area to get the parallelogram's area) is \(2(18 + 4)\) (assuming the appropriate base and height values for the triangles formed).

Answer:

\(2(18 + 4)\)