Answer:The area of the reduced backyard is 112.5 square feet
Explanation:
The initial length of the backyard is 40.5 feet long.
The initial width of the backyard is 25 feet wide.
In order to install a pool, the yard needs to be reduced by a scale of 1/3. This means that the new length of the backyard is would be
40.5 × 1/3 = 40.5/3 feet lonng
The new width of the backyard would be
25 × 1/3 = 25/3 feet wide
The backyard is rectangular in shape. Area of a rectangle is length × width. The area of the reduced backyard becomes
40.5/3 × 25/3 = 1012.5/9 = 112.5 square feet