Answer:
The correct answer is A. 60 square feet.
Explanation:
1. Let's review the data provided to us for solving the question:
The gazebo in Mr. Chang's backyard, according to the figure, is a square pyramid because its base is a square of 6 feet as length of its sides.
Length of the sides of the base = 6 feet
Slant length = 5 feet
Height = 4 feet
2. How much cloth, in square feet, will Mr. Chang need, assuming he does not need to replace the cloth at the bottom of the figure?
Area of a square pyramid = Base area + 1/2 Perimeter * Slant length
Replacing with the real values, we have:
Area of a square pyramid = 6 * 6 + 1/2 (6 + 6 + 6 + 6) * 5
Area of a square pyramid = 36 + 1/2 (24) * 5
Area of a square pyramid = 36 + 12 * 5
Area of a square pyramid = 36 + 60
Area of a square pyramid = 96 feet ²
3. But remember than Mr. Chang doesn't need to replace the cloth at the bottom of the gazebo.
So we need to subtract the area of the base to the area of the square pyramid:
Area of the square pyramid - area of the base
Area of the base = 6 * 6 = 36 feet ²
96 feet ² - 36 feet ² = 60 feet ²
The correct answer is A. 60 square feet.