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CHAPTER VI

DENOMINATE NUMBERS

Measures of Distance

12 Inches (in.)

= 1 Foot (ft.) 3 Feet

- 1 Yard (yd.) 52 Yards or 161 Feet 1 Rod (rd.) 320 Rods

1 Mile (mi.) 1 mi. = 320 rd. 1760 yd. = 5280 ft.

ORAL DRILL

1. How many inches in 3 ft.? in 5 ft. ? in 7 ft.? in 10 ft. ?

2. How many feet in 36 in.? in 48 in.? in 60 in. ? in 100 in. ?

3. How many feet in 5 yd. ? in 6 yd.? in 15 yd.? in 100

yd.?

4. How many feet in 4 rd.? in 6 rd.? in 2 rd. ? in 100 rd.?

5. How many yards in 2 rd.? in 4 rd.? in 6 rd.? in 100 rd.?

6. How many inches in 4 ft. 6 in. ? in 3 yd. 2 ft. ? 7. How many feet in 8 yd. 2 ft. ? in 9'yd. 2 ft. ?

8. What part of a foot is 9 in. ? is 2 in. ? is 3 in. ? is 4 in. ?

9. How many rods is į of a mile? I of a mile ? 1. of a mile?

10. What part of a mile is 80 rd. ? 32 rd. ? 64 rd. ?
11. What part of a mile is 220 yd. ? 440 yd. ? 880 yd. ?

12. At 16 cents a yard what will 2 yd. of ribbon cost? 51 yd.?

Other Measures of Distance

A nautical mile or knot is 6082.27 ft. or about 1.15 common miles.

A league is 3 nautical miles.
A fathom, used in measuring depths of water, is 6 feet.

A cable length, used for greater depths or distances, is 120 fathoms.

A hand, used in measuring heights of horses, is 4 inches.

A furlong, used occasionally in laying out race-courses, is 40 rods or one eighth of a mile.

Surface Measures

144 Square Inches (sq. in.) = 1 Square Foot (sq. ft.)
9 Square Feet

= 1 Square Yard (sq. yd.)
304 Square Yards

: 1 Square Rod (sq. rd.) 160 Square Rods

= 1 Acre (A.) 640 Acres

1 Square Mile (sq. mi.) 1 A. = 160 sq. rd. = 4840 sq. yd. = 43,560 sq. ft.

In roofing, flooring, painting, etc., the unit of area is 100 square feet; commonly called a square.

ORAL DRILL

1. How many square yards in 36 square feet? in 72 square feet?

2. How many square yards in į an acre? in an acre? 3. What part of an acre is 40 square rods ? 20 square rods ?

4. How many square yards in 54 square feet? in 84 square feet?

5. How many acres in a square mile? in į a square mile ? 6. In 2} square yards, how many square feet?

Exercise

1. A baseball diamond is 90 feet square. What is its area in square

feet? In square yards? In square rods ? 2. A tennis court is 78 feet long and 36 feet wide. What is its area in square feet? In square yards? In square rods?

3. A basketball court is 70 feet long and 50 feet wide. What is its area in square feet? In square yards? In square rods?

4. A football field is 330 feet long and 160 feet wide. What is its area in square feet ? In square yards ? In square rods? What fractional part of an acre does it contain ?

5. How many sods 16 inches square will be required to turf a lawn 170 feet long and 84 feet wide?

6. Find the cost of covering the floor of a hall 45 feet long and 30 feet wide with matting a yard wide at 70 cents a yard.

7. Find the cost of cementing the floor of a cellar 50 feet long and 28 feet wide at $ 1.10 per square yard.

8. If a square field is 1000 feet on a side, what is its area in acres ?

9. At $1 a square (i.e. 100 square feet) what will it cost to paint the four sides of a building 50 feet long, 20 feet wide, and 15 feet high ?

10. A baseball park 250 yards by 200 yards has a tight board fence around it 14 feet high. What will it cost to paint the outside of the fence at $.50 a square ?

11. If it cost $320 to fence a field 80 rods long and 60 rods wide, how much will it cost to fence a field 90 rods square ?

12. What will be the cost of plastering the ceiling of a room 22 feet by 18 feet at 12 cents a square yard?

13. What will be the cost of painting the outside of a house 52 feet long, 34 feet wide, and 22 feet high at 22 cents a square yard?

14. A piece of land 3 miles square can be cut up into how many 160-acre farms ?

15. How much will it cost to cover with concrete a cellar floor 40 feet by 20 feet at 90 cents a square yard ?

16. What will it cost to construct a 12-foot concrete sidewalk on two sides of a corner lot 40 feet by 150 feet if the sidewalk costs $ 1.10 per square yard ?

17. What will be the cost of a concrete sidewalk 12 feet wide around a city block 420 feet square at $ 1.20 per square yard ?

18. If bricks are 2 inches by 4 inches by 8 inches, what will be the cost at $10 a thousand for enough bricks to pave a piece of sidewalk 12 feet wide, 250 feet long, if the bricks are laid flatwise ?

19. At the same price what will it cost to pave the same sidewalk as in Example 18 if the bricks are laid edgewise? 20. What are the dimensions of a 40-acre rectangular field

that is four times as long as it is wide ?

21. The field represented in the figure was originally one mile square, but has had one quarter of it cut out of one corner. The remainder has been subdivided into four equal parts. Find the dimensions in rods of each of these parts.

Land Measures

640 Acres = 1 Square Mile

1 Mile Square 1 Section
36 Square Miles 1 Township

An acre in the form of a square is about 209 feet on a side.

[graphic]

are

Public Lands. A township is six miles square

and contains thirty-six sections, which

numbered from the northeast corner of the township across to the west, and back on the second tier to the east, then west again on the third tier, and so on, as indicated in the

SURVEYOR'S LEVEL AND TRI TSIT accompanying diagram.

Section 16 is designated as school land. In some of the newer states Section 36 is also designated as school land.

The diagram represents a section of land and its subdivisions, which are described as follows:

A is the north half of the section, and contains 320 acres.
B is the southwest quarter of the section, and contains 160 acres.

[blocks in formation]

C is the west half of the southeast quarter, and contains 80 acres. D is the northeast quarter of the southeast quarter, and contains

40 acres.

E is the southeast quarter of the southeast quarter, and contains 40 acres.

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