Lesson 2
Side Lengths and Areas
Let’s investigate some more squares.
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.
\frac{81}{2}
\sqrt{81}
9
\sqrt{9}
3
Problem 2
Write the exact value of the side length, in units, of a square whose area in square units is:
- 36
- 37
- \frac{100}{9}
- \frac25
- 0.0001
- 0.11
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}.
What is the side length of Square A? Square B? Square C? Explain how you know.
Problem 4
Find the area of a square if its side length is:
- \frac15 cm
- \frac37 units
- \frac{11}{8} inches
- 0.1 meters
- 3.5 cm
Problem 5
Here is a table showing the areas of the seven largest countries.
- How much larger is Russia than 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?
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 |
Problem 6
Select all the expressions that are equivalent to 10^{\text-6}.
\frac{1}{1000000}
\frac{\text-1}{1000000}
\frac{1}{10^6}
10^{8} \boldcdot 10^{\text-2}
\left(\frac{1}{10}\right)^6
\frac{1}{10 \boldcdot 10 \boldcdot 10 \boldcdot 10 \boldcdot 10 \boldcdot 10}