A rectangular prism has a base length of 6 units, base width of 5 units, and height of 4 units. The bases are shaded.

The lateral area is .

The area of the two bases together is .

The total surface area is

Part 1) The lateral area is

Part 2) The area of the two bases together is

Part 3) The surface area is

Step-by-step explanation:

Part 1) Find the lateral area

we know that

The lateral area of a prism is given by

where

P is the perimeter of the base

h is the height of the prism

so

----> perimeter of rectangle

---> given

substitute

Part 2) The area of the two bases together is?

The area of the rectangular base B is equal to

therefore

The area of the two bases together is

Part 3) The total surface area is

we know that

The surface area is equal to

substitute

.632

step-by-step explanation:

6 * 1/10 = 3/5

3*0.01 = 0.03

3/5 + 0.03 = .63

2*0.002 = .002

.63 + 0.002 = .632

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'.