Bunuel
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.
VERITAS PREP OFFICIAL SOLUTION:Question Type: What Is the Value? This question asks for the lateral area of the pyramid-shaped box. The lateral area represents the area of the faces of the polygon added together.
Given information in the question stem or diagram: The box is pyramid shaped and constructed with four lateral faces and an open bottom.
Statement 1: The base is a polygon with all sides of equal length and the perimeter of the base is 1 meter. This statement does not provide enough information to determine the area of the faces of the pyramid. While you know that each side of the polygon at the base is .25 meters, you have no idea about the height of the pyramid and thus the height of each lateral face. This is not sufficient so you can eliminate choices A and D.
Statement 2: The lateral faces are isosceles triangles that have the same size and shape. This statement is clearly insufficient by itself, as you are given no hard numbers. The question, then, is whether this statement helps you when combined with Statement 1. The answer is C or E.
Together: Taken together, the information still does not give you any idea about the height of the pyramid. If Statement 2 said that the lateral faces were equilateral triangles, then the answer would be C. However, this pyramid could be 3 meters high, or 10 meters high, greatly changing the area of the faces. Note: This question is a good example of the “prove E” concept. If you are going to choose
answer E, as you should in this problem, do so because you can identify the missing information, not just because the problem seems difficult. Here you are still missing the height of the pyramid so the correct answer is indeed E.