Rob is making a tent out of canvas in the shape of a square pyramid. Each side of the square base is 6 feet long, and the slant height is 7 feet. Which measurement BEST describes the amount of canvas needed to make this tent? (round to nearest whole number)
Responses
A 120 ft3
120 ft 3
B 76 ft3
76 ft 3
C 120 ft2
120 ft 2
D 76 ft2
76 ft 2
The amount of canvas needed would be the sum of the areas of each face of the pyramid. Each triangular face would have an area of (1/2)bh, where b is the base (6ft) and h is the slant height (7ft). Plugging in these values, we get (1/2)(6ft)(7ft) = 21ft^2 for each triangular face. There are four triangular faces, so the total area of canvas needed is 4(21ft^2) = 84ft^2. Rounded to the nearest whole number, the BEST measurement is therefore 84ft^2.
Answer: D) 76ft^2
120 feet
I'm sorry, can you please provide more context for this response? I am not sure what question you are referring to.
To find the amount of canvas needed to make this tent, we need to calculate the lateral surface area of the square pyramid.
The lateral surface area of a square pyramid can be found using the formula:
Lateral Surface Area = (Perimeter of the base) * (slant height) / 2
In this case, the perimeter of the base is the sum of all four sides of the square base. Since each side is 6 feet long:
Perimeter of the base = 6 ft + 6 ft + 6 ft + 6 ft = 24 ft
The slant height is given as 7 feet.
Now we can substitute these values into the formula to calculate the lateral surface area:
Lateral Surface Area = 24 ft * 7 ft / 2 = 168 ft²
Therefore, the amount of canvas needed to make this tent is approximately 168 square feet.
Among the given options, the measurement that best describes the amount of canvas needed is C) 120 ft².