Answer:
• Lateral area is the area of the sides of a 3-dimensional object, excluding the top and bottom bases. (Those bases are generally parallel to each other.) In the case of a cone or cylinder, it is the area of the curved surface. In the case of a pyramid, it is generally the area of the triangular faces. In the case of a cuboid, it is the area of the sides, excluding the top and bottom.
• Some examples are shown in the first attachment. An ambiguous case is shown in the second attachment. (For the ambiguous case, you would need to talk to the poser of the question to see what area they intend by "lateral area.")
Step-by-step explanation:
The total surface area of an object is the total area you would paint if you were to paint all surfaces of the object. The lateral area is the area you would paint if you did not paint the top or bottom surfaces (bases) of the object. For a pyramid or cone, the top base is a point, so has no area.
Some formulas are used for lateral area:
LA = πrs . . . . . cone with base radius r and slant-height s
LA = 2πrh . . . . cylinder with base radius r and height h
LA = Ph . . . . . . prism with base perimeter P and height h
LA = 1/2Ps . . . . pyramid with base perimeter P and slant height s
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About the ambiguous case in the second attachment
Generally, we take the "lateral area" of a pyramid to be the total area of its triangular faces. Here, the figure appears to be resting on one of its triangular faces, and the square base is uncovered at the side. This orientation suggests that the "lateral area" should include the area of the square, and exclude the area of one of the triangles.
Further adding to the ambiguity is the fact that the top flat surface might also be considered a "base" and excluded from the area calculation.
I don't have a definitive answer for this situation except to say that whoever posed the problem certainly had something in mind when they asked for the "lateral area" of this figure. They should be consulted as to their intent. (When this question was answered on Brainly, the square was included and one triangle was excluded. No feedback was provided to indicate whether that choice was "correct.") Personally, I might say this is a square pyramid and its lateral area is that of the four triangles: 352 m².
