A composite figure is a combination of shapes. To find the perimeter of a composite shape, you add the lengths of all the sides. However, you will need to use logic and common sense to find the lengths of any sides where measurements are missing.
For example, suppose we have a swimming pool that is a composite of two rectangles intersecting at one end to make an upside down L shape. The left side is for swimming lanes and the right side is the free play area. We know the area containing the swimming lanes is 100 meters long and 40 meters wide. We know the top of the shape, where both rectangles fit together, is 90 meters wide and the right edge of the free play area is 45 meters.
Before you can add all the sides to find the perimeter of the swimming pool, you need to find the two missing lengths, which we will call A and B. A is opposite the left side of the swimming lanes, which is 100 meters, and B is opposite the top edge of the shape that is 90 meters.
The right edge of the free play area is 45 meters. If you add 45 meters and side A, the measure would equal 100 meters. Therefore, we can find A by subtracting 45 from 100.
\(100-45 = 55\,{\rm{m}}\) \(A = 55 \space meters\)
The total width of both pools is 90 meters. The width of the swimming lanes is 40 meters. If you add 40 meters and side B, the measure must equal 90 meters, so you can find B by subtracting 40 from 90.
\(90-40 = 50\,{\rm{m}}\) \(B = 50 \space meters\)