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: Find full grid combination

Since all shapes cover 4 squares, total shapes needed: $\frac{144}{4} = 36$. A balanced full-fill combination:

Answer:

36a (or any combination where $4a + 4b + 4c + 4d + 4e = 144$, e.g., 9a, 9b, 9c, 9d, 0e; or 0a, 0b, 0c, 0d, 36e)

Note: Any combination where the sum of (number of each shape × 4) equals 144 will completely fill the grid. The simplest full-fill answer is using one shape exclusively, like 36 of shape e, as its 2x2 form tiles perfectly with no rotation needed.