ROOFING 263. 1. What will be the cost of shingles at $2.75 per M to cover the two sides of a roof, each side measuring 32 ft. long and 17 ft. from eaves to peak, if the shingles are laid 4 in. to the weather, estimating 1000 shingles per square (i.e. 10 x 10 (sq. ft.) = 100 sq. ft.)? 2. What will be the cost of shingling the above roof if the shingles are laid 4 in. to the weather? 5 in. to the weather? PAPERING 264. 1. At 32 a roll, what will be the cost of paper for a room 10 ft. wide, 12 ft. long, and 9 ft. high, allowing for 2 doors and 2 windows? NOTE. Wall paper is sold in rolls usually containing about 4 sq. yd. Paper hangers find the total area of the walls and ceiling, subtract 20 sq. ft. for each door and window, and divide the remainder by 33 sq. ft. for the approximate number of rolls. Parts of a roll are not sold. 2. Find the cost, at 30% a roll, of papering the walls of a room 14 ft. 6 in. x 13 ft. 4 in. and 12 ft. high, including bordering at 10 a yard, and hanging at 15¢ a roll, allowing for 4 windows and 3 doors. UNITED STATES PUBLIC LAND MEASURE 265. The United States public lands, before being offered for sale, are surveyed into tracts, 6 mi. × 6 mi. each, called townships. The townships are subdivided into sections of 1 sq. mi., 640 A., there being 36 of these sections in a township. Sections are subdivided in turn into quarter sections of 160 A. each, and the quarters into "halves" or eighties of 80 A. each, or quarters or forties of 40 A. each. The method of numbering sections in a township and the subdivisions of a section are illustrated on p. 175. The lines bounding a township extend due north and south, and east and west, and a line on a parallel of latitude is always established as a base. A line of townships extending north and south is called a range. The ranges are designated by their numbers east or west of the principal meridian, and the townships in each range by their number north or south of the base line. Lots which for any reason are irregular in form are designated as Lot 1, 2, 3, 4, etc., of a particular section. City and village plots are subdivided into blocks, and these again into smaller lots. 1. How much must be paid for the N.E. quarter of section 11 of a South Dakota township at $3 per acre? 2. If a speculator buys the northern half of a section of land and sells at various times the N.E. of N. W. 1, the N.W. 1 of N.E., the S.E. † of N.W. 1, and the N.E. of N.E. how many acres has he left? Draw a diagram to show what part of his half section he has left. 3. An agent bought a section of land at $5 an acre. He sold the south section at $7 an acre, the N.E. † of N.E. † at $8 an acre, and the N.E. of N.W. † at $6.50 an acre. How many acres did he sell? What part of the section had he left? SURVEYORS' MEASURE 266. For measuring land, surveyors use a measure called a chain (ch.), which is 4 rd. long and is divided into 100 links (1.). A square chain should be how many square rods in area? In 1 A. there are how many square rods? How many square chains? Since 10 sq. ch. equal 1 A., square chains may be changed to acres by moving the decimal point one place to the left, and acres may be changed to square chains by moving the decimal one place to the right. 267. Illustrative Example. A tract of land is 142 ch. by 48 ch. 17 1. Find the number of acres it contains. EXPLANATION. 48 ch. 17 1. = 48.17 ch. 142 x 48.17 sq. ch. sq. ch. : 684.014 A. = 6840.14 Ans. 684.014 A. 1. How many acres are there in a lot 56 ch. 24 1. long and 38 ch. 16 1. wide? 2. A pasture measures 68 ch. by 47 ch. 20 1. It contains many acres? how 3. At $75 an acre what is the value of a piece of land 106 ch. 34 1. × 87 ch. 44 1.? 268. To find one dimension of a rectangle, the area and the other dimension being given. Illustrative Example. A farm 160 rods long costs $3750 at $75 an acre. What is its width? EXPLANATION. To find the number of acres in the area we divide $3750 by $75, and find there are 50 acres. 50 acres = €8000 sq. rd. The area is 8000 sq. rd. Divide 8000 by the 160 in the given dimension and we Ans. 50 rd. wide. obtain 50, the number of rods in the other dimension. Written Exercise 269. 1. The area of a field is 20 acres. rd., what is its width? If its length is 64 2. Find the cost of fencing, at $11.25 a rod, a 36-acre field that is 96 rd. long. 3. How long is a walk 12 ft. wide, if its area is 84 sq. yd.? TRIANGLES 270. A triangle is a figure having 3 sides and 3 angles. A right-angled triangle has one right angle. TRIANGLE An obtuse-angled triangle has one obtuse angle. An equilateral triangle has 3 equal sides and 3 equal angles. An isosceles triangle has 2 equal sides. A scalene triangle has all its sides unequal. Vertex Base In these six kinds of triangles A, B, and Care named from their angles. D, E, and F are named from their sides. The base of a triangle is the side upon which it is supposed to rest. The angle opposite to the base is called the vertex. The altitude of a triangle is the perpendicular distance from the base, or the base produced, to the highest point in the triangle. The hypotenuse of a right-angled triangle is the side opposite the right angle. The perpendicular of a rightangled triangle is the line drawn at right angles to the base. Perpendicular AREA OF A TRIANGLE Hypotenuse Base size of ABC and place them as shown in DEFG. What is the name of the figure DEFG? To how many triangles of the size of ABC is DEFG equal? We may conclude therefore that: The area of a triangle is equal to half the area of a rectangle of the same base and altitude. |