A compound shape in geometry is a shape that has an irregular arrangement of sides or angles and must be broken down into simpler shapes before you can find the area or perimeter. "Compound shape" is not a rigorously defined geometric term, but rather a useful way of looking at shapes that are not straightforward to deal with. In theory, you can treat any shape as a compound shape, but it may not be useful to do so. For example; treating a square as two triangles makes it more complicated to find its area, not simpler.
To find the area of a compound shape, it is usually necessary to break the shape down into regular shapes with a known formula for area. In many cases, this is a fairly straightforward process, as any straight-edged areas can be divided into a set of rectangles and triangles, and rounded areas can be divided into sectors of circles and ovals, whose areas you can calculate separately and add together. In some cases, it may be necessary to measure a negative space and subtract its area from the total.
Finding the perimeter of a compound shape works in much the same way as finding the area. Divide the perimeter into straight lines and rounded lines, then add the lengths of each segment for the compound shape's total perimeter. In some cases, only partial information is available about the lengths of the compound shape's sides. In this case, you must infer the lengths of unknown sides from given sides. For example; if you know the total height of a "T" shape and the height of the cross bar, you may have to subtract the latter from the former to find the height of the upright stroke.
Compound shapes in a computer graphics program act as grouped objects, meaning a set of objects designated by the user, to get selected together and have certain edits like moving, resizing and fill styles applied to all of them simultaneously. A logo where every letter is a separate object is one example of a compound shape. Most graphics suites allow the user to group and ungroup objects at will, allowing you to alter individual components of the compound shape, then re-group the compound shape to edit it as a whole.