A square, where s is an odd integer, is divided into unit squares. All the unit squares along the edges and the 2 diagonals of a square are discarded. Find a fully simplified expression, in terms of s, for the number of unit squares remaining answer.

2 answers

there are 4(s-1) edge squares
there are an additional 2(s-2)-1 diagonal squares. Subtract that from the total area, and you have

s^2 - (4(s-1) + 2(s-2)-1)

You can simplify that...
How many unit squares are needed to cover the figures? Use the unit squares shown.

Figure A shows 2 squares. The sides of the larger square are approximately twice as long as the sides of the smaller square. The smaller square is labeled 1 square unit. Figure B shows 1 squares. The sides of the larger square are approximately 4 times as long as the sides of the smaller square. The smaller square is labeled 1 square unit.

A.
Figure A: 2 square units; Figure B: 4 square units

B.
Figure A: 2 square units; Figure B: 8 square units

C.
Figure A: 4 square units; Figure B: 8 square units

D.
Figure A: 4 square units; Figure B: 16 square units

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