To calculate the perimeter of a compound shape, you need to sum the lengths of all its straight and curved sides.

When tackling compound shapes, it’s essential to decompose the figure into simpler components. Begin by identifying and measuring all the straight sides. Utilize a ruler or any provided measurements to determine the lengths of these straight segments. Once you have these measurements, add them together to obtain the total length of the straight sides.

Next, turn your attention to the curved sides. If a curved side is part of a circle—such as a semicircle or a quarter circle—you’ll need to apply the formula for the circumference of a circle. The circumference of a full circle is expressed as:

where $r$ represents the radius. For a semicircle, you’ll use half of this formula:

For a quarter circle, the formula becomes:

After calculating the lengths of the curved sides, add these to the total length of the straight sides. The result will yield the total perimeter of the compound shape.

It is crucial to keep track of all parts of the shape and ensure that every side is included in your calculations. If the shape consists of multiple curved sections, calculate the length of each section individually, and then sum them all together.

By meticulously measuring and summing both the straight and curved sides, you can accurately determine the perimeter of any compound shape.