16. To pave a portion of a street 45 ft. 9 in. long at 22£ cts. per sq. ft. it cost £420.14. Determine the width of the street. 17. The cost of building a platform 43 ft. 9 in. long at 18| cts. per sq. yd. was £25.82. What was the width of the platform? EXERCISE CI. 199. Method of Indicating Work: 1. What is the area in acres of a rectangle 5760 in. long, 2376 in. wide. a. 5760X2376 sq. in. =area of rectangle in sq. in. . 5760X2376 _ , , . D. sq. ft. =area of rectangle in sq. ft. „ 5760X2376 , , , . c ——-—-—sq. yds. =area of rectangle in sq. yds. 144X9 H' & H 3 . 5760X2376 . 144X9 X30j-Sq' '=area of rectanSle in sq- rds. 5760X2376 , , . e. acres = area of rectangle in acres. 144X9X30^X160 6 200a Lines a, b, c, d were written to illustrate the principle of indicating work. Line e presents the indication of the work to be performed in the form the student should first write it. If 30£ were multiplied by 4, the product 121 being written as a denominator and 4 written to the right of 2376 with an X between, it would be in better form for cancellation. Perform the operation indicated on line e. 2. How many acres in a rectangle 3575 in. long, 2926 in. wide? 3 How many acres in a field 4840 in. long, 2576 in. wide? 4. How many acres in a field, 3968 in. long, 3520 in. wide? 5- How many acres in a field 3840 in. long, 256 ft. wide? 6. How many acres in a field, 8640 ft. long, 4320 ft. wide? 7. How many acres in a field, 528 yds. long 220 yds. wide? 8. Express in sq. rds. the area of a garden, 1326 in. long, 948 in. wide. 9. Express in sq. yds. the area of a hall, 1184 in. long, 332 in. wide. 10. How many acres in a field, 18 chains 75 links long, 14 chains 40 links wide? 18.75X14.4 = No. of sq. chains. 18.75X 1.44 = No. of acres. 11. How many acres in a field, 35 chains 25 links long, 25 chains 80 links wide? 12. How many acres in a field 16 chains 15 links long, 12 chains 60 links wide? 13. How many acres in a field in the form of a right angle triangle the base being 48 rds., the altitude 32 rds.? Note—See Figure 1. ^ This figure presents two rightangle triangles, which combined make a rectangle. The area of either the shaded part or the light B part is one-half the area of the rectangle A B c D. 14. How many sq. yds. in a right angle triangle, the base being 32 ft., the altitude 18 ft? 15. A field in the form of a right angle triangle is 36 rds. measuring from one of its acute angles to the right angle, and 18 rds. measuring from this point to the other acute angle. Determine area in acres? 16. Find the area of a right-angle triangle, the base being 18 ft., the altitude 16 ft. 17. Find the area of a right-angle triangle, the base being 32£ rd.s, the altitude 24 rds. 18. Find the area of a right-angle triangle, the base being 36 yds., the altitude being 36f yds. 19. A field in the form of a right-angle triangle is 46 rds., measuring from one of its acute angles to the right angle, and 48 rds. 6 ft. long, measuring from the other acute angle to the right angle. What is the area of the field? 2. What is the value at $125 per acre? Note—Have pupi1s draw the figure and write answers inside the 1ines, and mark it "area of triang1e." SURVEYOR'S MEASURE. The Surveyor's, or Gunter's, chain is generally used in surveying land. It is 4 poles, or 66 feet in length, and is divided into 100 links. TABLE. inches make 1 link, marked 1. 4 rods = 66 ft. = 100 links = 1 chain, marked c. 80 chains make 1 mile, marked mi. 1 square chain makes 16 square rods, or perches. 10 square chains make 1 acre, marked A. 201. In the accompanying figure the opposite sides are parallel, but two of the angles are acute angles, and two are ob■ D tuse angles. The parallelogram Figure 2. A B c D equals in area the PARALLELOGRAM. _ . i . „ „ „ rectangle A B F E. The line A D is longer than the line A E. The area of a parallelogram is therefore the product of the altititude and the length. EXERCISE CII. 1. What is the area of a parallelogram 75 ft. long, the altitude being 63 ft.? Express area in sq. yds. 2. What is the area of a parallelogram the length of the longer sides being 32 ft. 9 in., the altitude being 16 ft. 6 in.? 3. The length of the sides of a parallelogram is 148 ft., the ends 76 ft., the altitude 54 ft. What is the area in sq. yds.? 4. A field in the form of a parallelogram is 36 rds., measured on the longer sides, and 34 rds., measured on the shorter sides; the altitude is 32 rds. What is the area in acres? 5. What would it cost to fence this field at $2.25 per rd.? 6. The same length of fence would enclose a rectangle 36 rds. long, 34 rds. wide. What is the difference in area between the two? (Problems 4 and 6.) 7. A field is 60 rds. on one of its parallel sides, a shorter parallel side extending at an acute angle is 48 rds. 6 ft. long; the altitude is 36 rds. What is the area in acres? 8. What would be the cost of fencing the field described in problem 7 at $1.15 per rd.? 9. What is the area of a rectangle 80 rds. long, 36 rds. wide? 10. How much more would it cost to fence a field 36 rds. sq. than to fence a field 81 rds. long, 16 rds. wide at $1.25 per sq. rd.? Observe the areas are equal. ^—•j 202. The side A B is par allel to the side c D. The dotted line shows the °H G c way m which the trapezoid is Figure 3. changed to a rectangle of equal Trapezoid. area. If the line D c be 60 ft. 60 X 40 and the line A B 40 ft., — ft. equals the length of A the equivalent rectangle. To find the area of a trapezoid, change the figure to an equivalent rectangle. One-half the sum of the parallel sides multiplied by the altitude, or the shortest distance between the parallel sides, is the area of a trapezoid. EXERCISE CIII. 1. What is area insq. yds. of a trapezoid the parallel sides of which are respectively 35 ft. and 48 ft., the altitude being 18 ft.? 2. One side of a trapezoid is 56 yds. 2 ft. long, the shorter parallel side 44 yds. 1 ft. long, the altitude 33 ft. What is the area? 3 The parallel sides of a trapezoid are 48 rds. 6 ft., and 32 rods. 9 ft., the altitude is 28 rds. 6 ft. What is the area, expressed in acres? 4. The parallel sides of a trapezoid are 32 rds 12 ft. and 24 rds. 10 ft. long, the altitude is 24 rds. What is the area? 5. The parallel sides of a trapezoid are 35 ft. 8 in., and 27 ft. 10 in., the altitude is 22 ft. 6 in. What is the area in sq. yds.? 6. The parallel sides of a trapezoid are 196 in. and 144 in., the altitude 9 ft. 6 in. What is the area in sq. yds.? THE AREA OF WALLS AND CEILINGS. EXERCISE CIV. 1. How many sq. yds. in the surface of the 4 walls and ceiling of a room 18 ft. 9 in. long, 15 " 10 " wide, 11" 5 " high? Total area in sq. yds., 120.73 1* ft 34T\ is the length of one side and one end, which multiplied by 2 gives the length or perimeter of the 4 walls The length multiplied by the height, and this product multiplied by \ gives the area in sq. yds. All the work should be indicated as on line b. Note—The indication of work shown on the 1eft is for explanation only. Area of cei1ing is shown on line c. 204. The i11ustration showing- how to use the extra s1ip of paper for the recording of the computations involved wi11 suggest to the worker its uti1ity. In actua1 app1ication this sheet of paper wou1d be made to cover line c. Then the work appearing here cou1d be turned under, thus giving a new edge to place under 1ine c. and preserving the work for review in case an error was made in computation. Submit to your teacher the indicated work and the resu1ts. |