Area Conversions - Homeschool Giveaways

Area Conversions Many people are familiar with the U.S. Customary units of measure, either because they are using them now or have used them in the past. However, the metric system, while commonly used in many parts of the world, is not always as familiar to people in the United States. The metric system began as a result of the French National Assembly asking the French Academy of Sciences to try to standardize the system of weights and measures that had become so confused in France. In 1791, work on the new system was begun, and by 1795, all metric units had been set and identified in France. By 1799, the new units were declared the legal standards for every measurement used in France. In 1875, an international conference met in Paris to set up an International Bureau of Weights and Measures. Meetings are held to reconsider the way the units have been determined, and the system has been refined over the years. Today, the metric system, based on units of 10, has been officially adopted by most of the countries in the world. Below are two tables. The first shows the equivalency of 1 square inch, 1 square foot, 1 square yard, and 1 square mile to common metric measures. The second shows the equivalency of 1 square millimeter, 1 square centimeter, 1 square meter, and 1 hectare to common U.S. Customary measurements. For ease in use, we have rounded the measurements to two decimal places where possible.

Square

Square

Square Meters

Hectares

1 Square Inch

645.16 mm2

6.45 cm2

0.0006 m2

---

1 Square Foot

92903.04 mm2

929.03 cm2

0.09 m2

0.000009 ha

1 Square Yard

836127.4 mm2

8361.27 cm2

0.84 m2

0.00008 ha

1 Square Mile

---

---

2589988 m2

259.00 ha

Square Inches

Square Feet

Square Yard

Square Miles

1 Square Millimeter

0.002 in2

0.00001 ft2

0.000001 yd2

---

1 Square Centimeter

0.16 in2

0.001 ft2

0.0001 yd2

---

1 Square Meter

1550 in2

10.76 ft2

1.20 yd2

---

1 Hectare

15500031 in2

107639.1 ft2

11959.90 yd2

0.004 mi2

How do you convert between the two systems when the need arises? Use the standard methods of conversion shown in the tables above to solve the following practice problems. ©2016 Bonnie Rose Hudson WriteBonnieRose.com

Activity One: If we know that 1 square inch (in.2) = 645.16 square millimeters (mm2) or 6.45 square centimeters (cm2), find the answers to the following problems. 9 in.2 = __________ mm2

16 in.2 = __________ cm2

15 in.2 = __________ mm2

33 in.2 = __________ cm2

21 in.2 = __________ mm2

56 in.2 = __________ cm2

29 in.2 = __________ mm2

42 in.2 = __________ cm2

35 in.2 = __________ mm2

39 in.2 = __________ cm2

Activity Two: Now that you have your answers for the above problems, convert them into different metric measurements. For example, we see that 9 in.2 equals 5806.44 mm2. There are 100 square millimeters in a square centimeter. To convert from square millimeters to square centimeters, you divide the number of millimeters by 100, so 9 in.2 also equals 58.06 cm2. To convert from square centimeters to square millimeters, you multiply the number of square centimeters by 100. Using your answers in the exercise above, convert the square millimeter answers to square centimeters, and the square centimeter answers to square millimeters. Round your answers to two decimal places. The first one is done for you. 9 in.2 = 5806.44 mm2 or 58.06cm2

16 in.2 = __________ cm2 or __________mm2

15 in.2 = __________ mm2 or __________cm2

33 in.2 = __________ cm2 or __________mm2

21 in.2 = __________ mm2 or __________cm2

56 in.2 = __________ cm2 or __________mm2

29 in.2 = __________ mm2 or __________cm2

42 in.2 = __________ cm2 or __________mm2

35 in.2 = __________ mm2 or __________cm2

39 in.2 = __________ cm2 or __________mm2

©2016 Bonnie Rose Hudson WriteBonnieRose.com

Activity Three: If we know that 1 cm2 equals .16 in.2, convert the following: 159 cm2 = __________ in.2

582 cm2 = __________ in.2

208 cm2 = __________ in.2

694 cm2 = __________ in.2

375 cm2 = __________ in.2

785 cm2 = __________ in.2

427 cm2 = __________ in.2

861 cm2 = __________ in.2

543 cm2 = __________ in.2

917 cm2 = __________ in.2

Activity Four: Using the fact that 1 square foot (ft.2) equals .09 square meters (m2) or 929.03 square centimeters (cm2), find the answers to the following problems: 1. You have a room that measures 12 ft. in length by 12 ft. in width. What is the area, in square feet, of the room? What would the area be in square meters? What would it be in square centimeters?

2. If your home has a front yard that measures 50 feet in length by 30 feet in width, what would the area be in square feet? What would it be in square meters?

3. You are in charge of renting a large dining hall for a banquet. You have a choice between a dining hall that measures 20 feet in length by 30 feet in width or one that measures 10 meters in length by 7 meters in width. Which dining hall is larger?

4. You found a piece of material in your mother’s sewing room that measures 3 feet by 2 feet. The project you are working on requires 6,000 cm2. Do you have enough material for your project?

5. How many square centimeters of carpeting would you need to make a floor mat that measures 2.5 feet in length by 1.5 feet in width? ©2016 Bonnie Rose Hudson WriteBonnieRose.com

Activity Five: Now, using the fact that 1 hectare (ha) = .004 square miles (mi.2), compute the following, rounding to two decimal places: 95 ha = __________ mi.2

25 ha = __________ mi.2

154 ha = __________ mi.2

73 ha = __________ mi.2

222 ha = __________ mi.2

14 ha = __________ mi.2

87 ha = __________ mi.2

37 ha = __________ mi.2

43 ha = __________ mi.2

349 ha = __________ mi.2

Activity Six: Using the fact that 1 square yard (yd.2) equals .84 square meters (m2), do the following problems: 1. You have a parking lot that measures 19 yards in length by 36 yards in width. How many square yards of parking space does it contain? How many square meters of parking space does it contain?

2. You are required to report your property measurements in square meters. You know that your property measures 207 feet by 306 feet. You also know that there are 3 feet in a yard. How many square yards does your property contain? How many square meters does it contain?

3. The store you work at sells a special material that is made 1 yard wide, so each yard that is bought is a square yard. Someone buys 27 feet of material. Knowing there are 3 feet in a yard, how many square yards did they buy? How many square meters did they buy?

4. You live in an old house that has one room which measures 27 feet in length by 18 feet in width. You go to buy carpeting and find that it is sold by the square meter. Knowing there are 3 feet in a yard, how many square yards does the room contain? How many square meters?

5. You have an odd-shaped piece of property that contains one rectangle measuring 6 yards in length by 12 yards in width, then narrows to another rectangle that measures 4 yards in length by 10 yards in width. How many square yards total does it contain? How many square meters? ©2016 Bonnie Rose Hudson WriteBonnieRose.com

Activity Seven: Knowing that 1 square mile (mi.2) = 259 hectares (ha), do the following problems: 70 mi.2 = _______ ha

30 mi.2 = _______ ha

24 mi.2 = _______ ha

9 mi.2 = _______ ha

19 mi.2 = _______ ha

6 mi.2 = _______ ha

3 mi.2 = _______ ha

21 mi.2 = _______ ha

52 mi.2 = _______ ha

14 mi.2 = _______ ha


Answer Key: Activity One: 9 in.2 = 5806.44 mm2

16 in.2 = 103.2 cm2

15 in.2 = 9677.4 mm2

33 in.2 = 212.85 cm2

21 in.2 = 13548.36 mm2

56 in.2 = 361.2 cm2

29 in.2 = 18709.64 mm2

42 in.2 = 270.9 cm2

35 in.2 = 22580.6 mm2

39 in.2 = 251.55 cm2

Activity Two: 9 in.2 = 5806.44 mm2 or 58.06cm2

16 in.2 = 103.2 cm2 or 10320 mm2

15 in.2 = 9677.4 mm2 or 96.77 cm2

33 in.2 = 212.85 cm2 or 21285 mm2

21 in.2 = 13548.36 mm2 or 135.48 cm2

56 in.2 = 361.2 cm2 or 36120 mm2

29 in.2 = 18709.64mm2 or 187.1 cm2

42 in.2 = 270.9 cm2 or 29090 mm2

35 in.2 = 22580.6 mm2 or 225.81cm2

39 in.2 = 251.55 cm2 or 25155 mm2

Activity Three: 159 cm2 = 24.44 in.2

582 cm2 = 93.12 in.2

208 cm2 = 33.28 in.2

694 cm2 = 111.04 in.2

375 cm2 = 60 in.2

785 cm2 = 125.6 in.2

427 cm2 = 68.32 in.2

861 cm2 = 137.76 in.2

543 cm2 = 86.88 in.2

917 cm2 = 146.72 in.2

Activity Four: 1.

144 ft.2 or 12.96 m2 or 133780.32cm2

2.

1500 ft.2 or 135 m2

3. The first dining hall is 54 m2. The second dining hall is 70 m2. The second dining hall (measuring 10 meters by 7 meters) is the larger of the two. 4.

No, the material is only 5574.18 cm2.

5.

3483.86 cm2


Activity Five: 95 ha = 0.38 mi.2

25 ha = 0.1 mi.2

154 ha = 0.62 mi.2

73 ha = 0.29 mi.2

222 ha = 0.89 mi.2

14 ha = 0.06 mi.2

87 ha = 0.35 mi.2

37 ha = 0.15 mi.2

43 ha = 0.17 mi.2

349 ha = 1.4 mi.2

Activity Six: 1.

684 yd.2 or 574.56 m2

2.

7038 yd.2 or 5911.92 m2

3.

9 yd.2 or 7.56 m2

4.

54 yd.2 or 45.36 m2

5.

112 yd.2 or 94.08 m2

Activity Seven: 70 mi.2 = 18130 ha

30 mi.2 = 7770 ha

24 mi.2 = 6216 ha

9 mi.2 = 2331 ha

19 mi.2 = 4921 ha

6 mi.2 = 1554 ha

3 mi.2 = 777 ha

21 mi.2 = 5439 ha

52 mi.2 = 13468 ha

14 mi.2 = 3626 ha
