# Illustrative Mathematics Grade 8, Unit 8, Lesson 2: Side Lengths and Areas

Learning Targets:

• I can explain what a square root is.
• I understand the meaning of expressions like √25 and √3.
• If I know the area of a square, I can express its side length using square root notation.

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Illustrative Math

#### Lesson 2: Side Lengths and Areas

Let’s investigate some more squares.

Illustrative Math Unit 8.8, Lesson 2 (printable worksheets)

#### Lesson 2 Summary

The following diagram shows how when given the area of a square, we can express its side length using square root notation.

#### Lesson 2.1 Notice and Wonder: Intersecting Circles

What do you notice? What do you wonder?

#### Lesson 2.2 One Square

1. Use the circle to estimate the area of the square shown here:
2. Use the grid to check your answer to the first problem.

#### Are you ready for more?

One vertex of the equilateral triangle is in the center of the square, and one vertex of the square is in the center of the equilateral triangle. What is x?

#### Lesson 2.3 The Sides and Areas of Tilted Squares

1. Find the area of each square and estimate the side lengths using your geometry toolkit. Then write the exact lengths for the sides of each square.
2. Complete the tables with the missing side lengths and areas.
3. Plot the points, (s,a), on the coordinate plane shown here.
Open Applet
4. Use this graph to estimate the side lengths of the squares in the first question. How do your estimates from the graph compare to the estimates you made initially using your geometry toolkit?
5. Use the graph to approximate √45.

#### Lesson 2 Practice Problems

1. A square has an area of 81 square feet. Select all the expressions that equal the side length of this square, in feet.
2. Write the exact value of the side length, in units, of a square whose area in square units is:
3. Square A is smaller than Square B. Square B is smaller than Square C.
The three squares’ side lengths are √26, 4.2, and √11.
What is the side length of Square A? Square B? Square C? Explain how you know.
4. Find the area of a square if its side length is:
5. Here is a table showing the areas of the seven largest countries.
How much more area is there in Russia than in Canada?
The Asian countries on this list are Russia, China, and India. The American countries are Canada, the United States, and Brazil. Which has the greater total area: the three Asian countries, or the three American countries?
6. Select all the expressions that are equivalent to 10-6.

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.