Lesson 2

Side Lengths and Areas

Problem 1

A square has an area of 81 square feet. Select all the expressions that equal the side length of this square, in feet.

A:

\(\frac{81}{2}\)

B:

\(\sqrt{81}\)

C:

9

D:

\(\sqrt{9}\)

E:

3

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

Problem 2

Write the exact value of the side length, in units, of a square whose area in square units is:

  1. 36
  2. 37
  3. \(\frac{100}{9}\)
  4. \(\frac25\)
  5. 0.0001
  6. 0.11

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

Problem 3

Square A is smaller than Square B. Square B is smaller than Square C. 

The three squares’ side lengths are \(\sqrt{26}\), 4.2, and \(\sqrt{11}\).

There are 3 differently sized squares labeled, from left to right, “A,” “B” and “C.” The squares are arranged from smallest to largest, so that “A” is the smallest square and “C” is the largest.

What is the side length of Square A? Square B? Square C? Explain how you know.

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

Problem 4

Find the area of a square if its side length is:

  1. \(\frac15\) cm
  2. \(\frac37\) units
  3. \(\frac{11}{8}\) inches
  4. 0.1 meters
  5. 3.5 cm

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

(From Unit 8, Lesson 1.)

Problem 5

Here is a table showing the areas of the seven largest countries.

  1. How much larger is Russia than Canada?
  2. 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?

country area (in km2)
Russia \(1.71 \times 10^7\)
Canada \(9.98 \times 10^6\)
China \(9.60 \times 10^6\)
United States \(9.53 \times 10^6\)
Brazil \(8.52 \times 10^6\)
Australia \(6.79 \times 10^6\)
India \(3.29 \times 10^6\)

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

(From Unit 7, Lesson 15.)

Problem 6

Select all the expressions that are equivalent to \(10^{\text-6}\).

A:

\(\frac{1}{1000000}\)

B:

\(\frac{\text-1}{1000000}\)

C:

\(\frac{1}{10^6}\)

D:

\(10^{8} \boldcdot 10^{\text-2}\)

E:

\(\left(\frac{1}{10}\right)^6\)

F:

\(\frac{1}{10 \boldcdot 10 \boldcdot 10 \boldcdot 10 \boldcdot 10 \boldcdot 10}\)

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

(From Unit 7, Lesson 5.)