I have a garden that is shaped like a triangle on the left side and a semi-circle on the right side. The base of the triangle is also the diameter for the semi-circle. The diameter of the circle is 13ft and the height of the triangle is 6ft. Please draw a picture and label your measurements before working out the problem. What is the total area of my garden?

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.