A cone is a 3 dimensional shape and therefore does not have an "area" the way a circle or a square does.
3 dimensional shapes such as cones can have "surface area" and "cross-sectional area". Note that 3 dimensional shapes can have an infinite number of different cross sectional areas because you can define an infinite number of cross sections.
So I'll assume you are asking about the surface area of a cone.
The surface area is the sum of the area of the base (circle) and the actual cone part.
Let's assume the base has a radius "r" and the length of the "angled" part of the cone (from the outside of the base to the peak of the cone) is "L".
So the base has an area of:
(pi)*r^2 (where ^ means "to the power of")
and the cone part has a surface area of:
(pi)*r*L
Therefore the total surface area of the cone is:
base + cone
(pi)*r^2 + (pi)*r*L
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