Area in real life

I want to make geometry more interesting to my students by making it feel more "real". In an attempt to do so, I created the following exercise:

Lillian wanted to reseed her lawn after installing a new gazebo. The area that needs to be reseeded is represented by the shaded part of the diagram below. Help her find the area that she needs to reseed.

Part I: What is the area of the gazebo (the octagon)? Assume that the gazebo is the shape of a regular octagon. Remember, the apothem is the distance from the center to an edge. The distance of the gazebo from edge to edge is 4.8 meters.  

 Part II: What is the area of the whole yard (the rectangle)?  

 Part III: What is the area of the lawn that needs to be reseeded? Show your work.  

In the future, I would like to develop this activity further by giving students a set yard size and allowing students to shop for their own hexagon or octagon-shaped gazebo to put in the yard (which will change the area of the lawn that needs to be reseeded). This will give them more freedom in the assignment and allow them to use their creativity.