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

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50