We've seen some ways we can explore the side lengths and angles of shapes. Another way we'll measure size of a shape is by the **area** it covers.

These three techniques are critical, and they're flexible strategies, not formulas.

We can draw in lines or even a whole grid to cut up shapes and patterns of shapes.

After cutting up a shape, we can rearrange the pieces so that calculating the area becomes simply a matter of counting squares.

We can sometimes make and then rearrange extra copies of a shape so that all of the pieces combined can make a single square or rectangle.

**The big theme here is that rectangles and squares are key because we can find their areas very quickly!**

In this $9 \times 6$ rectangle, is more area shaded or not shaded?

What fraction of the rectangle's area is taken up by the regular hexagon?

What is the area of the shaded part of this $8 \times 5$ rectangle?

Even when shapes have curved sides, we can still reason with and compare their areas.

The centers of the circles and a corner of the square are all at the same point. The square's side length is $10 \text{ m}.$

What is the area of the shaded part of the diagram?

Which figure has the **largest** shaded area?

When solving this problem, you can assume that:

- The three squares above are all the same size.
- Each curve in the three figures is a circle segment from a circle with diameter equal to the side length of the square.