-- The amount of paper you'd have if you cut the figure out.
-- The amount of carpet you need to completely cover the figure.
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a sphere
It is incorrect to say that sphere has lateral area. First sphere do not have sides like other geometric figure. In fact a line or plane can intersect the surface of a sphere in just one point. Sphere has no lateral side. It is enough to say surface area of sphere than lateral surface area of the sphere.
It is the surface area
You need to find the area of each two dimensional surface on the figure. Do you have a specific figure in mind?
A quadrilateral does not have a surface area because it is not a voluminous figure.