What is the perimeter of a compound shape with lengths 4 cm, 6 cm, 8 cm, and 10 cm?

The perimeter of the compound shape is 28 cm.

To find the perimeter of a compound shape, you need to add up the lengths of all its sides. In this case, the shape has sides measuring 4 cm, 6 cm, 8 cm, and 10 cm. The perimeter is simply the total distance around the shape, which means you sum these lengths together.

So, let's do the calculation step-by-step:
\[ 4 \, \text{cm} + 6 \, \text{cm} + 8 \, \text{cm} + 10 \, \text{cm} = 28 \, \text{cm} \]

Therefore, the perimeter of the compound shape is 28 cm. This method works for any compound shape as long as you know the lengths of all its sides. Just remember to add them all together to get the total perimeter. This is a fundamental concept in geometry and is essential for solving more complex problems involving shapes and their properties.