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A landscaper is creating a bench for a pool deck. A model of the bench is shown in the image. A rectangular prism with dimensions of 7 feet by 3 feet by 4.8 feet. Part A: Find the total surface area of the bench. Show all work. (6 points) Part B: The landscaper will cover the bench in ceramic tiles except for the bottom that is on the ground. If the tiles cost $0.89 per square foot, how much will it cost to cover the bench? Show all work. (6 points

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Why, hello there! Let's embark on a magical journey through the land of geometry. In this world, our hero is a bench, destined to be the throne of poolside leisure, a rectangular prism shaped dream with dimensions of 7 feet long, 3 feet wide, and 4.8 feet tall.

Part A:

To understand our bench's majesty, we'll need to calculate its total surface area. Each face of this rectangular royal is a rectangle itself. Our gallant hero has six sides: 2 sides measuring 7 feet by 3 feet (the top and bottom), 2 sides of 7 feet by 4.8 feet (the front and back), and 2 sides of 3 feet by 4.8 feet (the ends).

To find the area of each rectangle, we multiply its length by its width. So:

- The top and bottom are 7 feet by 3 feet. Therefore, their area is 7*3 = 21 square feet. Since there are 2 of these sides, their total area is 2*21 = 42 square feet.

- The front and back are 7 feet by 4.8 feet. Therefore, their area is 7*4.8 = 33.6 square feet. Again, because we have 2 of these sides, their total area is 2*33.6 = 67.2 square feet.

- The ends are 3 feet by 4.8 feet. Their area is 3*4.8 = 14.4 square feet. And because we have 2 of these sides, their total area is 2*14.4 = 28.8 square feet.

Now, let's add these all up for our bench's total surface area:

Total Surface Area = 42 (top and bottom) + 67.2 (front and back) + 28.8 (ends) = 138 square feet

Our magnificent bench, in all its prismatic glory, has a total surface area of 138 square feet.

Part B:

But hold on, our bench is destined for grandeur! It will be cloaked in the finest ceramic tiles, save for the part that rests on the ground. For this, we must deduct the area of the bottom (7*3 = 21 square feet) from our total surface area.

So, the area to be tiled = Total Surface Area - Area of the bottom = 138 square feet - 21 square feet = 117 square feet

Each square foot of tile costs $0.89, making the cost a simple multiplication:

Cost to cover the bench = Area to be tiled * cost per square foot = 117 square feet * $0.89/square foot = $104.13

And so, for a mere sum of $104.13, our bench will be adorned with the splendor of ceramic tiles, ready to bask in the sunlight by the pool deck, and await the tired swimmer who seeks comfort. What a whimsical journey through the realm of mathematics we have undertaken! And it's only the beginning...

User Parag Kadam
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