Question

unit 5 lesson 2

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 a total of $12 \times 12 = 144$ unit squares.

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, we can use a combination that fills the entire grid. $144 \div 4 = 36$ total shapes. A balanced combination that works (rotating/reflection allowed to fit) is:

Answer:

9a, 9b, 9c, 9d, 0e

(Note: This combination uses 9 of each of shapes a-d, totaling $9 \times 4 \times 4 = 144$ squares, which fills the entire 12x12 grid. Other valid combinations that fill the full grid are also acceptable.)