Question

by making a net of a cube, we construct a shape with six identical squares connected along their sides. this shape is called a hexomino. laying these six squares in various patterns but still connected along at least one side can result in 35 possible patterns. here are a few examples: a. b. c. 1. which of the hexominoes, a, b, and c, can be folded to form a closed cube? 2. make at least five more hexominoes.

Explanation:

Step1: Recall cube - net rules

A cube - net is a two - dimensional shape that can be folded to form a three - dimensional cube. There are 11 distinct nets of a cube. A net of a cube must have no overlapping squares when folded and all faces must be accounted for.

Step2: Analyze option A

Option A is a valid cube net. It can be folded in such a way that all six faces of the cube are formed without any overlapping.

Step3: Analyze option B

Option B cannot be folded into a closed cube. When trying to fold it, there will be overlapping of squares or some faces will not be properly formed.

Step4: Analyze option C

Option C is a linear arrangement of six squares. It cannot be folded into a closed cube as there is no way to close the shape to form a three - dimensional cube without cutting or overlapping in an improper way.

For the second part, here are five more hexominoes that can be drawn (it is best to draw them on paper, but we can describe them):

1. A shape with three squares in a row on the bottom and one square above each of the left - most, middle, and right - most squares of the bottom row.
2. Two rows of three squares each.
3. A row of four squares with one square above the second and one square above the third square of the row of four.
4. A row of three squares with two squares above the middle square of the row of three, one on top of the other.
5. A row of two squares with four squares above them in a 2 - 2 formation.

Answer:

1. A.
2. (Descriptions of five hexominoes are given above)