Please show all the work For #9, fill in the missing information for the following trapezoids. SHOW YOUR WORK to solve for the missing value.
9.
height =
b1 = 20 cm
b2 = 21 cm
area = 205 cm2

We know that the area of trapezoid is = ( a+b/2 ) × h

Whereas, a is base ( b1 ) and b is another base ( b2 ) and h is height. Given area of trapezoid is = 205 cm²

So the answer of yours question is, Height of trapezoid = 10 cm.

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'.