Question

What is the total area of all three gardens if each garden is in the shape of a square with a 3-foot by 3-foot section removed from each of the four corners, and one garden is shown with a larger square of side length 16 feet?

A. 220 square feet
B. 256 square feet
C. 660 square feet
D. 768 square feet

Answer 1

The total area of all three gardens is 768 square feet (D).

Step-by-step explanation:

To find the total area of the gardens, we first need to determine the area of each individual garden. The shape of each garden is a square with a 3-foot by 3-foot section removed from each of the four corners. Therefore, the side length of the larger square (without the corners removed) is 16 feet, and the side length of the smaller square (after removing the corners) is
`\(16 - 2 * 3 = 10\)` feet. The area of each smaller square is
`\(10^2 = 100\)` square feet.

Since there are three gardens in total, we multiply the area of one smaller square by 3 to get the total area:
`\(100 * 3 = 300\)` square feet. Additionally, we need to add the area of the larger square, which is
`\(16^2 = 256\)` square feet. Therefore, the total area is
`\(300 + 256 = 556\)`square feet.

However, the question provides answer choices in square feet that differ from our calculated value. The closest match is option D, which is **768 square feet**. Upon reevaluating our calculations, we find an error in the explanation. The correct total area is
`\(100 * 3 + 256 = 456\)` square feet. The closest match to this corrected value among the answer choices is option **C: 660 square feet**. I apologize for any confusion caused by the mistake in the initial calculation.