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: Find the base and height of parallelogram \(ABCD\)

From the graph, for parallelogram \(ABCD\), the base \(AB = 2\) units (since \(A(3,2)\) and \(B(5,2)\), \(\vert5 - 3\vert=2\)), and the height \(h_1=4\) units (the vertical distance from \(y = 2\) to \(y = 6\)).
Using the formula for the area of a parallelogram \(A = base\times height\), \(A_{ABCD}=2\times4 = 8\) square units.

Step2: Find the base and height of parallelogram \(EFGH\)

For parallelogram \(EFGH\), the base \(EF = 2\) units (since \(F(-5,2)\) and \(E(-3,2)\), \(\vert- 3-(-5)\vert=2\)), and the height \(h_2 = 4\) units (the vertical distance from \(y = 2\) to \(y = 6\)).
Using the formula for the area of a parallelogram \(A = base\times height\), \(A_{EFGH}=2\times4=8\) square units.

Answer:

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