⦁ Leo designs a stand for the new statue on display at the local library. The stand is in the shape of a right trapezoidal prism. The base of the prism has an area of 3 ft2, and the prism stands 3.2 feet high. As Leo paints the stand, he calculates the surface area of the stand to be 35 ft2.
⦁ Leo is asked to purchase roping that will be used to close off the area around the statue. He purchases a length that is five times the perimeter of the stand in roping.
⦁ How much roping does he purchase?
⦁ Leo plans to add gold leaf to the sides of the stand but not to the two bases.
⦁ What percent of the area of the stand will have gold leaf? Round your answer to the nearest whole number.

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abiolataiwo2015 abiolataiwo2015 · Answer 1 · 2022-04-28T18:04:41+02:00

If the surface area of the stand to be 35 ft². The number of ropes purchase is 45.3125ft and Percent of stand area is 83%.

Given:

Base area=3ft²

Height=3.2 feet

Surface area=35ft²

a. Number of ropes

Surface area=2×Base area×Base perimeter×Height

Base perimeter(BP):

35=2×3+BP×3.2

35=6+3.2BP

Collect like term

3.2BP=35-6

3.2BP=9

Divide both side by 3.2BP

BP=29/3.2

BP=9.0625ft

Number of ropes=5×9.0625ft

Nimber of ropes=45.3125ft

b. Percent of stand area:

Percent of stand area=(9.0625ft×3.2)÷35ft²

Percent of stand area=29ft²÷35ft²×100

Percent of stand area=82.857ft×100

Percent of stand area=83% (Approximately)

Therefore the number of ropes purchase is 45.3125ft and Percent of stand area is 83%.

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