Question

how do the areas of the parallelograms compare? the area of parallelogram abcd is 2 square units greater than the area of parallelogram efgh. the area of parallelogram abcd is 4 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 \(AB = 4\) units (from \(x = 2\) to \(x = 6\)) and the height is \(4\) units (from \(y = 2\) to \(y = 6\)).
So, \(A_{ABCD}=4\times4 = 16\) square units.

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

For parallelogram \(EFGH\), the base \(EH = 4\) units (from \(x=- 4\) to \(x = - 0\)) and the height is \(4\) units (from \(y = 2\) to \(y = 6\)).
So, \(A_{EFGH}=4\times4=16\) square units.

Answer:

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