Two rectangles are drawn, as shown. Find the area of their overlap, which is shaded.

Step-by-step explanation:

Look at the picture.

Shadded region is a parallelogram.

The formula of an area of a prarallelogram:

We have the height h = 2.

Calculate the base.

Green triangles are congruent.

Use the Pytgagorean theorem:

We have:

Substitute:

Therefore the base is:

Calculate the area:

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i