Answer:
The area of parallelogram ABCD is equal to the area of parallelogram EFGH.
Step-by-step explanation:
Given
Parallelogram ABCD
[tex]A = (4,2)[/tex]
[tex]B = (7,2)[/tex]
[tex]C =(4,6)[/tex]
[tex]D = (1,6)[/tex]
Parallelogram EFGH
[tex]E =(-2,2)[/tex]
[tex]F = (-5,2)[/tex]
[tex]G = (-6,6)[/tex]
[tex]H = (-3,6)[/tex]
Required
Compare the areas of both parallelograms
The area of a parallelogram is:
[tex]Area =Base * Height[/tex]
So: To do this, we plot ABCD and EFGH on a grid, then we measure the base and the height of both.
See attachment 1 for ABCD
In (1), we have:
[tex]Base = 3\ units[/tex]
[tex]Height = 4\ units[/tex]
So, the area is:
[tex]A_1 = 3 * 4[/tex]
[tex]A_1 = 12[/tex]
See attachment 2 for EFGH
In (2), we have:
[tex]Base = 3\ units[/tex]
[tex]Height = 4\ units[/tex]
So, the area is:
[tex]A_2 = 3 * 4[/tex]
[tex]A_2 = 12[/tex]
By comparison, they both have the same areas
