Question

1. use as many of the following shapes in any combination that you need to in order to fill in as much of the 12 by 12 grid as you can. you may rotate or reflect a shape if it helps. write your answer showing how many of each shape you used using the letters that identify the shape.

example combination: 3a, 5b, 10c, 2d, 6e

Explanation:

Step1: Calculate grid total area

The 12x12 grid has total squares: $12 \times 12 = 144$

Step2: Note each shape's area

Shape a: 4 squares, Shape b: 4 squares, Shape c: 4 squares, Shape d: 4 squares, Shape e: 4 squares

Step3: Maximize full grid coverage

Since all shapes cover 4 squares, total shapes needed: $\frac{144}{4} = 36$. We can use a simple combination that fills the grid completely.

Answer:

36a, 0b, 0c, 0d, 0e

(Note: This combination uses only shape a, rotated/reflected as needed to tile the 12x12 grid perfectly, as 12 is divisible by 4, the length of shape a. Other valid full-coverage combinations exist, e.g., 0a, 0b, 0c, 0d, 36e, since shape e is a 2x2 tile that also perfectly tiles a 12x12 grid.)