Find the perimeter of compound shapes when all side lengths are known or can be easily determined [M7]

Calculating the perimeter of compound shapes can be a straightforward task when all side lengths are known or can be deduced with simple methods. To determine the perimeter of such shapes, one must add together the lengths of all the sides that outline the figure. For example, if a compound shape consists of rectangles and triangles joined together, the perimeter would be the total length of the external sides without counting any internal dividing lines. It's essential to ensure that all measurements are in the same units before summing them up to avoid any discrepancies in the final calculation.

When presented with a compound shape on a grid, students can employ various strategies to find the lengths of all sides. If the shape is composed of standard geometric figures, such as rectangles and triangles, the students can use known formulas to calculate individual perimeters and then combine them, remembering to subtract any common sides that are not part of the overall outline. For more complex shapes, it may be necessary to break down the figure into familiar shapes, calculate each one's perimeter, and then piece them together, being mindful of shared sides. The key is to systematically work through the shape, ensuring no side is overlooked and all are measured correctly.