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For the perimeter of a polygon you add the sides to find the total distance around the shape. For area, you multiply using the various formulas for different polygons.
You would find the area of the inside and outside shape (pretending that the inside shape was not in the outside shape). then, you would take the area of the outside shape and subtract the area of the inside shape.
Shape of what ?
To find the area, first divide the shape into regular, simple shapes. Then use formulas to find the area of the smaller, regular shapes. Lastly, add up all the smaller areas to find the area of the original shape.
Such as? If you can break the shape up into triangles you can find the area that way. Or, you can get into calculus-based equations if you have an equation for the random shape.