Question

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 4 ft^2 and the prism stands 2.4 feet high. As Leo paints the stand, he calculates the surface area of the stand to be 32 ft^2.

(a) 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?


(b) 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​.

Answer 1

Leo needs to purchase 30 ft of roping and 88% of the area of the stand will have gold leaf.

Step-by-step explanation:

To find the amount of roping Leo needs to purchase, we first need to find the perimeter of the stand. A trapezoidal prism has 4 sides, two of which are the bases. Since the base has an area of 4 ft^2, we can find the length of one base by taking the square root of 4, which is 2 ft. The other base will have the same length. The other two sides of the prism are the trapezoids, where the top base is half the size of the bottom base. So, the top base length is 1 ft. The perimeter of the stand is then 2 + 2 + 1 + 1 = 6 ft. Since Leo purchases a length that is five times the perimeter of the stand, he needs to buy 6 x 5 = 30 ft of roping.

To find the area of the sides that Leo plans to cover in gold leaf, we need to subtract the area of the two bases from the total surface area. The surface area is given as 32 ft^2, so the area of the two bases is 4 ft^2. The area of the sides that will have gold leaf is then 32 - 4 = 28 ft^2. To find the percentage of the area with gold leaf, we divide the area with gold leaf by the total surface area and multiply by 100. (28 / 32) x 100 = 87.5%. Rounded to the nearest whole number, the percentage of the area with gold leaf is 88%.