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Take the circumference and multiply it by it's height to get the lateral surface area.
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Perhaps a rectangular prism
Uisng the lateral area and tha radius, you should be able to find the height of the cone. Using the height and radius as the legs of a right triangle, use the Pythagorean Theorem. The hypotenuse is the slant height.
Using Pythagoras' theorem the height of the equilateral triangle works out as about 7 cm and so with the given dimensions it would appear to be quite difficult to work out the lateral area.