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The base of the roof of a building has a pentagonal shape. The roof is constructed as a regular pyramid with a pentagon

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The base of the roof of a building has a pentagonal shape. The roof is constructed as a regular pyramid with a pentagon

by BTGmoderatorDC » Wed Feb 19, 2020 5:57 pm

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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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Source: — Data Sufficiency |
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Re: The base of the roof of a building has a pentagonal shape. The roof is constructed as a regular pyramid with a penta

by deloitte247 » Sat Feb 22, 2020 10:48 pm

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What is the total area of the lateral segment of the roof
Given that roof = Regular pyramid and base of the roof have a pentagonal shape
Total surface Area = Base Area + Lateral Area $$When\ Larteral\ Area=\frac{\left(perimeter\cdot slant\ height\right)}{2}$$ $$Perimeter=\left(length\ of\ one\ edge\ of\ the\ base\right)\cdot\left(no\ of\ edges\right)$$
To find the lateral area, we need to know the perimeter and the 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 INSUFFICIENT.

Statement 2
The faces of the pyramid are equal triangle
Any pyramid with regular polygon as base will always have equal triangle as the lateral surface. This information was already provided from the question stem . Since statement has no new information , then statement 2 is INSUFFICIENT.

Combining both statements together
The only new information available from both statement is the parameter of the base , since the slant height of the triangle is still unknown then both statements together are NOT SUFFICIENT.

$$Answer\ is\ Option\ E$$
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