A pyramid-shaped box to protect a plant is constructed with 4 lateral faces and an open bottom. What is the lateral area of the box?

(1) The base of the pyramid is a polygon with all sides of equal length, and the perimeter of the base is 1 meter.
(2) The lateral faces are isosceles triangles that have the same size and shape.


Kudos for a correct solution.
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Question : Lateral Area = ?

Statement 1: The base of the pyramid is a polygon with all sides of equal length, and the perimeter of the base is 1 meter.
Since the Number of sides in base =4
Perimeter i.e. 4*Side = 1
i.e. Side = 1/4
But the height of the pyramid is unknown rendering to different values of lateral faces for different height of Pyramid. Hence,
NOT SUFFICIENT

Statement 2: The lateral faces are isosceles triangles that have the same size and shape.
But the height of the pyramid and Side of base quadrilateral are unknown rendering to different values of lateral faces for different height of Pyramid. Hence,
NOT SUFFICIENT

Combining the two statements
Side of Base = 1/4
All faces are Isosceles but the heights can be different rendering different values of Area of Lateral Surface Area. Hence,
NOT SUFFICIENT

Answer: option E
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"Careless reading of questions is too dangerous unless you are lucky to get correct answer by luck"

Have made some changes in explanations. I hope You would find it appropriate now.
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

A pyramid-shaped box to protect a plant is constructed with 4 lateral faces and an open bottom. What is the lateral area of the box?

(1) The base of the pyramid is a polygon with all sides of equal length, and the perimeter of the base is 1 meter.
(2) The lateral faces are isosceles triangles that have the same size and shape.

Looking at the original condition, there are numerous variables in a pyramid-shaped box (3 for triangles and 4 for squares), so we need that much number of equations. However, the conditions only provide us with 2 equations in total, giving a high chance that (E) is going to be the answer
Looking at the conditions, even if we combine the 2 conditions, we cannot know the length of an edge of any face, making the conditions insufficient and the answer becomes (E).

For cases where we need 3 more equation, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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