This worksheet is designed to teach students how to write the area of circles and compound shapes both as a decimal and in terms of Pi (something both the SAT/PSAT and ACT will require them to do). I have found that students have been taught and know how to write their answers as decimals (using 3.14 for Pi), but many have never been taught how to leave an answer in terms of Pi. Leaving an answer in Pi form, as you probably know, is a more exact answer and requires students to think about problems a little differently. Sometimes they will have to combine two separate Pi terms into one term.
Compound shapes are difficult for many students. They have a difficult time seeing the shapes and planning out how to find the area. I always teach students to start off by making a plan. List the shapes they see, and tell whether they will be adding or subtracting the shapes. This is also true of the shaded region shapes. They then write the formula for each shape they listed, and then compute the area. Finally, they combine the areas (add or subtract depending on what shape they are doing).
I have found this to be a great worksheet to help teach my students critical thinking skills as well as how to systematically plan/organize/solve a problem.
I have included an answer key for this worksheet.