The pattern shown here is made from concentric circles cut into quarters. Find the total area of the shaded regions. I’ll give brainliest if you got the right answer :)

First, while this can be solved by calculating each individual area, let's do it in a smarter way.

Notice that there are two outer parts shaded, and two inner parts shaded.

When we add all of those, we get half of the larger circle.

So we only need to calculate the area of the larger circle and then divide it by two.

Remember that the area of a circle is:

A = pi*r^2

where:

pi = 3.1416

r = radius of the circle.

In the image, we can see that the diameter of the larger circle is 8ft.

And we know that r is half of the diameter, then:

r = 8ft/2 = 4ft

Now we can replace those values in the area of the larger circle and get:

A = 3.1416*(4ft)^2 = 50.27 ft^2

Half of that is:

A/2 = 21.14 ft^2.

That is the area of the shaded regions.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.