Final answer:
To find the total area around the section of land with a 2.5-foot wide enclosure of pebbles running around a garden of flowers, calculate the area of the larger square and subtract the area of the smaller square. The total area is 50 square feet.
Step-by-step explanation:
To find the total area around the section of land that has a 2.5-foot wide enclosure of pebbles running around a garden of flowers, you can calculate the area of the larger square and subtract the area of the smaller square. The larger square represents the total area of the enclosure and the smaller square represents the area of the garden of flowers.
The side length of the larger square is the sum of the side length of the garden of flowers and twice the width of the enclosure, which is 2.5 feet. So the side length of the larger square is 2.5 + 2(2.5) = 7.5 feet.
The area of the larger square is 7.5^2 = 56.25 square feet. The area of the smaller square, which represents the area of the garden of flowers, is the side length of the garden of flowers squared, which is (2.5)^2 = 6.25 square feet.
Therefore, the total area around the section of land is 56.25 - 6.25 = 50 square feet.