The lateral area of the given pyramid is 108 cm².
Any three-dimensional figure's lateral surface area is its side surface area.
In the question, we are asked to find the lateral area of the given pyramid, whose base is a regular hexagon, with a side length of 3 cm, and the slant height of the pyramid is 12 cm.
To determine the lateral area, we determine the area of one lateral face, and then multiply it by the number of lateral faces in the pyramid.
The number of lateral faces = sides of the base = 6 {Since the base is a regular hexagon}.
Area of a lateral face = (1/2)*base*height {Since its a triangle},
or, area of a lateral face = (1/2)*3*12 {Since the base is the side length of the base, and the height is the slant height},
or, area of a lateral face = 18 cm².
Thus, the lateral area of the pyramid = 6 * 18 cm² = 108 cm².
Thus, the lateral area of the given pyramid is 108 cm².
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