Question

Three squares. The first square is labeled with side length 1 inch on the vertical side and 1 inch on the horizontal side. The second square is labeled with side length one half inch on the vertical side and one half inch on the horizontal side. The third square is labeled with side length 2 inches on the vertical side and 2 inches on the horizontal side. What do you notice about the areas of the squares? Write your observations. Consider the statement: “A square with side lengths of 13 inch has an area of 13 square inches.” Do you agree or disagree with the statement? Explain or show your reasoning.

Answer 1

The area is the side lengths squared or multiplied by themselves. The three squares have very different areas based on their side lengths. I disagree that a square with 13 inch side length will have area 13. It will have area 13*13=169 square inches.

Explanation:

The area of a square is A=s*s.

1st: A = 1*1 = 1 square inches.

2nd: A=1/2*1/2 = 1/4 square inches

3rd: A =2*2 = 4 square inches.

The area of a square with 1 unit side length is still 1. But a square whose side is less than 1 has a very small area and the square whose side length is greater than 1 has a much larger area. The area of a square is the square of its side length or its side length times itself.

Knowing this, a square with side length 13 will not have area 13 but area 169.