Final answer:
The question tests estimating the area and perimeter in units of square yards. Dimensional analysis ensures proper use of units; area is measured in square units, perimeter in linear units.
Step-by-step explanation:
The question is testing knowledge of estimating the area and perimeter of a shape using square units. To estimate the area, you count the number of squares that cover the shape, since each square is given as 9 yd2. The estimated area is then this number multiplied by 9. For the perimeter, you would measure the length around the shape using the sides of the squares as your guide. If a side of the square corresponds to 'a' yards, then the perimeter would be the total length around the shape in yards.
In this context, concepts such as dimensional analysis and units of measurement are being applied. Dimensional analysis helps us to ensure that our calculations make sense unit-wise. The units of area are always in square units, such as square yards (yd2), while the units of perimeter are in linear units, like yards (yd). Therefore, it is important not to mix these up, as doing so would be dimensionally inconsistent.
For example, to remember the formula for the area of a circle, we would not confuse circumference (2πr) with area (πr2). Using dimensional consistency, we know that the circumference would be a linear measure (units of length), while the area must be a square measure (units squared).