Mrs. Trace is purchasing an umbrella with a slant height of 4 feet. There are a variety of such umbrellas to choose from. Mrs. Trace will choose the umbrella with the greatest lateral surface area. Which will she choose?

a. A pink umbrella is shaped like a regular pentagonal pyramid with a side length of 3 feet. Find the lateral surface area.

b. A yellow umbrella is shaped like a regular hexagonal pyramid with a side length of 2.5 feet. Find the lateral surface area.

c. A blue umbrella is shaped like a regular octagonal pyramid with a side length of 2 feet. Find the lateral surface area.

answer is 144

step-by-step explanation:

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

no

step-by-step explanation:

6^2 or 36

step-by-step explanation:

6000n

6×1000n

6×10^3 n

so we need 6n need to be a perfect cube

so n has to be 6^2 so that 6n is 6^3

what i'm saying is if you let n be 6^2 you have 6^3×10^3 or 60^3 which is a perfect cube