Question

how do the areas of the parallelograms compare?
the area of parallelogram abcd is 4 square units
greater than the area of parallelogram efgh.
the area of parallelogram abcd is 2 square units
greater than the area of parallelogram efgh.
the area of parallelogram abcd is equal to the area
of parallelogram efgh.
the area of parallelogram abcd is 2 square units
less than the area of parallelogram efgh.

Explanation:

Step1: Calculate the area of parallelogram \(ABCD\)

The formula for the area of a parallelogram is \(A = base\times height\).
For parallelogram \(ABCD\), the base \(AB\) (or \(DC\)): \(AB=\vert7 - 3\vert= 4\) units, and the height (vertical distance between \(AB\) and \(DC\)): \(\vert6 - 2\vert = 4\) units.
So, \(A_{ABCD}=4\times4 = 16\) square units.

Step2: Calculate the area of parallelogram \(EFGH\)

For parallelogram \(EFGH\), the base \(FE\) (or \(GH\)): \(FE=\vert- 1-(-5)\vert = 4\) units, and the height (vertical distance between \(FE\) and \(GH\)): \(\vert6 - 2\vert=4\) units.
So, \(A_{EFGH}=4\times4 = 16\) square units.

Answer:

The area of parallelogram \(ABCD\) is equal to the area of parallelogram \(EFGH\).