The smiths are installing a rectangular sandbox measuring 4 feet by 6 feet with an area of 8 square feet in their 18 foot by 34 foot backyard. the sandbox must be at least 4 feet from the fence that surrounds the backyard so that mrs. smith can access her flower beds, and it cannot be placed within 2 feet of the house, the 6 foot by 8 foot rectangular patio attached to the back door, or the oak tree in the backyard. on graph paper with a distance between gridlines representing 2 feet, mr. smith draws a scale drawing of the backyard and shades in the area in which the sandbox cannot be placed. both the boundaries of the backyard and regions in which the sandbox must be placed are the intersections of gridlines. if the corners of the sandbox must also be at the intersections of gridlines, how many different locations in the backyard are possible for the placement of the sandbox?