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Roots of Squares

9.5.1 Roots of Squares

9.5.1 • Roots of Squares

Warm Up

Here are some squares whose vertices are on a grid.

Three squares are drawn on grid paper. On the left is a square labeled "A" that has a side length of 3 units and is oriented upright. In the center is a smaller square labeled "B." Square B is tilted up one unit showing that its side length lies on the diagonal of a unit square. On the right, another square labeled "C" is also tilted. Here, the side length of C shows that its length lies along a right triangle that is one unit tall and three units long.

Find the area and the side length of each square.

1.

What is the area of Graph A?

9 square units.

2.

What is the side length of Graph A?

3 units.

3.

What is the area of Graph B?

2 square units.

4.

What is the side length of Graph B?

Compare your answer:

22 units

5.

What is the area of Graph C?

10 square units.

6.

What is the side length of Graph C?

Compare your answer:

1010 units