Side Lengths and Areas

Student Summary

The area of square ABCDABCD is 73 units2.

Since the area is between 82=648^2 = 64 and 92=819^2 = 81, the side length must be between 8 units and 9 units. We can use tracing paper to trace a side length and compare it to the grid, which also shows the side length is between 8 units and 9 units.

When we want to talk about the exact side length, we can use the square root symbol. We say “the square root of 73,” which is written as 73\sqrt{73} and means “the side length of a square with area 73 square units.” It is also true that (73)2=73\left( \sqrt{73} \right)^2=73.

Tilted square ABCD with side lengths of square root of 73 units 

Visual / Anchor Chart

Standards

Building On
6.EE.1

6.EE.A.1

6.G.1

6.G.A.1

Addressing
8.NS.2

8.NS.A.2

8.NS.A

8.NS.A

Building Toward
8.EE.2

8.EE.A.2

8.EE.2

8.EE.A.2

8.EE.2

8.EE.A.2