How do I solve for the shaded area?

Option A:

Area of the shaded part = 99 cm²

Solution:

Length of the rectangle = 15 cm

Width of the rectangle = 9 cm

Area of the rectangle = length × width

                                    = 15 × 9

                                    = 135 cm²

Area of the rectangle = 135 cm²

Side of the square = 6 cm

Area of the square = side × side

                                = 6 × 6

                                = 36 cm²

Area of the square = 36 cm²

Area of the shaded part = Area of the rectangle – Area of the square

                                        = 135 cm² – 36 cm²

                                        = 99 cm²

Area of the shaded part = 99 cm²

Option A is the correct answer.

Hence the area of the shaded part of the figure is 99 cm².

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'.