Lesson 2: Side Lengths and Areas

Side Lengths and Areas

Student Summary

The area of square $ABCD$ is 73 units².

Since the area is between $8^2 = 64$ and $9^2 = 81$ , 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 $\sqrt{73}$ and means “the side length of a square with area 73 square units.” It is also true that $\left( \sqrt{73} \right)^2=73$ .

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

Visual / Anchor Chart

Standards

Building On

6.EE.1

Write and evaluate numerical expressions involving whole-number exponents.

6.G.1

Find area of triangles, trapezoids, and other polygons by composing into rectangles or decomposing into triangles and quadrilaterals. Apply these techniques in the context of solving real-world and mathematical problems.

Addressing

8.NS.2

Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions.

8.NS.A

No additional information available.

Building Toward

8.EE.2

Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Know square roots of perfect squares up to 225 and cube roots of perfect cubes up to 125. Know that the square root of a non-perfect square is irrational.