Manhattan Prep
The base of the roof of a building has a pentagonal shape. The roof is constructed as a regular pyramid with a pentagon as its base. What is the total area of the lateral segments of the roof?
1) The base of the pyramid has a perimeter of 30 meters.
2) The faces of the pyramid are equal triangles.
OA E
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The base of the roof of a building has a pentagonal shape. The roof is constructed as a regular...
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deloitte247
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What is the total area of the lateral segments of the roof?
Given that roof = regular pyramid and base of the roof has a pentagonal shape
Total surface area = base area + lateral area
$$Where\ lateral\ area=\frac{perimeter\cdot no.\ of\ edges}{2}$$
To find the lateral area, we need to know the perimeter and slant height.
Statement 1: The base of the pyramid has a perimeter of 30 meters.
This statement provides us with the perimeter of the base but there is no information regarding the slant height value. So the total area of lateral segments cannot be estimated, hence, statement 1 is NOT SUFFICIENT.
Statement 2: The faces of the pyramid are equal triangles.
Any pyramid with a regular polygon as base will always have equal triangles as the lateral surfaces. This information is already provided from the question stem. Since this statement has no new information, then statement 2 is NOT SUFFICIENT.
Combining both statements together:
The only new information available from both statements is the perimeter of the base, since the slant height of the triangle is still unknown, then, both statements combine together are NOT SUFFICIENT.
Therefore, the correct answer is option E.
Given that roof = regular pyramid and base of the roof has a pentagonal shape
Total surface area = base area + lateral area
$$Where\ lateral\ area=\frac{perimeter\cdot no.\ of\ edges}{2}$$
To find the lateral area, we need to know the perimeter and slant height.
Statement 1: The base of the pyramid has a perimeter of 30 meters.
This statement provides us with the perimeter of the base but there is no information regarding the slant height value. So the total area of lateral segments cannot be estimated, hence, statement 1 is NOT SUFFICIENT.
Statement 2: The faces of the pyramid are equal triangles.
Any pyramid with a regular polygon as base will always have equal triangles as the lateral surfaces. This information is already provided from the question stem. Since this statement has no new information, then statement 2 is NOT SUFFICIENT.
Combining both statements together:
The only new information available from both statements is the perimeter of the base, since the slant height of the triangle is still unknown, then, both statements combine together are NOT SUFFICIENT.
Therefore, the correct answer is option E.
