Activity Valerie is remodeling her home. She decides to replace the old carpet in the living room and wants to know how much carpet she needs. You can see from the diagram of the living room that this is not a simple shape. Complete the steps below to find the area of the room, which is the amount of carpet Valerie needs for her project.

Part A
Help Valerie decompose the shape into the fewest simple shapes. Which shapes can you divide the figure into? How many of each shape do you get?
Part B
In how many different ways can you divide the shape to get the same number and type of shapes you obtained in part A?
Part C
On a separate piece of paper, draw the different ways you can divide the given shape into simpler shapes. Describe each result.
Part D
What are the dimensions of the simple shapes you obtained in part C? List dimensions for all your decompositions (sets of shapes).
Part E
Using the dimensions from part D, find the area of each simple shape. Do this for all your decompositions (sets of shapes).
Part F
Add the areas of the simple shapes you found in part E to find the area of the composite shape. Do this separately for both decompositions. What do you notice about the two answers?
Part G
What is the amount of carpet Valerie needs for her living room?