EXAMPLES. 6. Required the area of a square whose side is 5 feet 9 inches ? Ans. 35ft. 9 in.9''. 7. Required the area of a rectangle, whose sides are 56 feet, and 18 feet 6 inches? Ans. 1036 feet. 8. Required the area of the rhombus or rhomboides, whose length is 12 feet 6 inches, and its height 9 feet 3 inches ? Ans. 115 ft. 7 in. 6. II. To find the area of a triangle. RULE-Multiply the base by the perpendicular height, and half the product will be the area. EXAMPLES. 9. Required the area of the triangle whose base is 10 feet. 9 inches, and height 7 feet 3 inches. Ans. 38 ft. 11 in. 7. 10. What is the area of a triangle, whose base is 18 feet 4 inches, and height 11 feet 10 inches? Ans. 108 ft. 5 in. 8'. III. To find the area of a trapezium. RULE-Multiply the diagonal by the sum of the two perpendiculars falling upon it from the opposite angles, and half the product will be the area. EXAMPLES. 11. What is the area of a trapezium whose diagonal is 108 feet 6 inches, and the perpendiculars 56 feet 3 inches, and 60 feet 9 inches? Ans. 6347 feet, 3 inches. 12. Required the area of a trapesium whose diagonal is 60 feet, and the perpendiculars 50 feet and 40 feet? Ans. 2700 feet. IV. To find the area of a trapezoid, or quadrangle, two of whose opposite sides are parallel. RULE-Multiply the sum of the parallel sides by the perpendicular distance between them, and half the product will be the area. EXAMPLES. 13. Required the area of a trapezoid whose parallel sides are 25 feet 6 inches, and 18 feet 9 inches, and the perpendicular distance 10 feet, 5 inches. Ans. 230 ft 5 in 7en 14. How many square feet are in a plank 13 one end, and 15 at the other, the length ben ches? Ans. art of the hests markrked AW. 19 feet, 1 inch SB. No. 1 . OF THE CIRCLE. 1. The diameter of a circle being given to find the circumference; or, the circumference being given to find the diameter. : RULE. 7: 22 so is the diameter: to the circumference ; or, 113 355: so is the diameter: to the circumference. 22 7 so is the circumference: to the diameter. or, 355: 113: so is the circumference: to the diameter. EXAMPLES. 1. The diameter of a circle is 9 feet: What is the circum ference ? Ans. 28.27 feet. 2. If the diameter of a circle be 10 feet: What is the circumference? Ans. 31.41 feet. 3. If the circumference of a circle be 354, what is the di ameter ? 112.681. 4. The circumference of the globe is known to be 25000 miles Required its diameter ? Ans. 7958 nearly. Ans. II. To find the area of a circle. RULE-Multiply half the circumference by half the diam eter, and the product will be the area. EXAMPLES. 5. What is the area of a circle whose diameter is 42, and circumference 131.946 ? Ans. 1385.433. 6. What is the area of a circle whose diameter is 10 feet 6 inches, and circumference 31 feet 6 inches? Ans. 82 ft. 8 in. SOLIDS. I. To find the solidity of a cube. RULE-Multiply the side of the cube by itself, and that product again by the side, and it will give the solidity. EXAMPLES. 1. Required the solidity of å cube whose sides are 15 inches Ans. 1ft. 11 in. 5, 2. The side of a cube is 25 feet 6 inches: required th lidity? Ans. 16581 ft. 4 in re II. To find the solidity of a parallelopipedon. ches RULE-Multiply the length by the breadth, and th 6d. duct again by the depth, or heighth, and it will give high, lidity. feet ot 3. Requed the solidity of the parallelopipedon, whose length is 8 et, breadth 45 feet, and depth 6 feet? Ans. 243 ft. vard 20 4. What is the solid content of a block of marble, whose length is 10 feet, its breadth 5 feet, and the depth 32 feet ? Ans. 2011 ft. III. To find the solidity of a triangular prism. RULE-Multiply the area of the base into the perpendicu lar height, and the product will be the solidity. EXAMPLES. 5. Required the solidity of the triangular prism whose length is 10 feet, and either of the equal sides of one of its equilateral ends 2 feet? Ans. 27.063 ft. 6. Required the solidity of a prism whose length is 18 feet, and one side of the equilateral end 14 feet? Ans. 17.50859 ft. IV. To find the solidity of a cylinder. RULE-Multiply the area of the base by the perpendicular height, and the product will be the solidity. EXAMPLES. 7: What is the solidity of the cylinder, the diameter of whose base is 30 inches, and the height 50 inches? Ans. 20.4531 ft. 8. What is the solidity of the cylinder whose height is 20 feet, and the circumference of its base 20 feet also? Ans. 636.64 V. To find the solidity of a pyramid or cone. RULE-Multiply the area of the base by, the perpendicular altitude, and the product will be the solidity. EXAMPLES. 9. Required the solidity of a square pyramid, each side of whose base is 30, and the perpendicular height 20? Ans. 6000. 10. What is the solidity of a cone, the diameter of whose base is 18 inches, and its altitude 15 feet ? Ans. 8.83575 ft. If the circumference of the base of a cone be 40 feet, he height 50 feet: What is the solidity? Ans. 2120 ft. per To find the solidity of the frustum of a pyramid or cone. E-Add into one sum the area of both ends, and the proportional between them; multiply the sum by the 13.dicular height, and the product will be the solidity are 25% EXAMPLES. Wil icular hat is the solidity of the frustum of a quare pyra side of the greater end being 18 inches that of the sser end 15 inches, and the height 60 inches? Ans 1680 inche 1 13. What is the solidity of the frustum of the cone, the diameter of the greater end being 4 feet, that of the lesser end 2 feet, and the altitude 9 feet? Ans. 65.9736. 14. What is the solidity of the frustum of a cone, the circumference of the greater end being 40, that of the lesser end 20, and the length or height 50? Ans. 3713.64. VII. To find the solidity of a sphere or globe. RULE-Multiply the cube of the diameter by .5236, and the product will be the solidity. ter. EXAMPLES. 15. Required the solidity of a sphere of 10 inches diame Ans. 523.6. 16. How many solid miles are in the terraqueous globe, its diameter being 7958 miles Ans. 263883017937.1232. ARTIFICERS WORK. 1. Glaziers & Masons flat work is measured by the square foot. EXAMPLES. 1. What is the content of 12 windows, each measuring 3 feet 10 inches long, and 2 feet 8 inches broad: what will the glazing come to at 25 cents per foot? Ans. 30 2. There is a house with 3 tier of windows, 4 in a tier, the height of the first tier is 6 feet 6 inches, the second 5 feet 3 inches, and the third 4 feet 9 inches, the breadth of each window is 3 feet 9 inches: what will the glazing come to at 2s. 8d. per foot? Ans, 331. 3. What is the price of a marble slab whose length is 64 feet, and breadth 34 feet, at $1 per foot? Ans. $21.12 II. Painting, Plaistering, Paving, &c. is measured by the yard square. RULE-Divide the square feet by 9 the quotient will be the number of square yards. EXAMPLES. 4. What will the paving of a street come to at 12 cents per yard, the length of the street being 176 feet, and the breadth 56 feet? Ans. $139.116. 5. What is the content of a piece of wainscotting in square yards, that is 9 feet 6 inches in height, and 8 feet 3 inches broad, and what will it come to at 12s. per yard. Ans. 8 ft. 6. 4. 6 and 51. 4s. 6d. 6. There is a room 84 feet round, and 9 feet 6 inches high, in which are three windows, each 6 feet high and 3 feet 5 inches wide, and the fire-place 4 feet by 4 feet: I demand how many yards of paper, half yard wide will hang it ? 7. What will the plaistering of yard come to, supposing the length 34 20 feet! a Ans. 160 yds. 6 in. Ans. III. Flooring, Partitioning, Roofing, Tyling, &c. is measured by the square of 100 feet. RULE-Divide the area in square feet by 100, the quotient will be the number of squares.“, EXAMPLES. 8. In 120 feet 6 inches in length, and 12 feet 9 inches in height of partitioning, how many squares? Ans. 15 sq. 36 ft. 4 in. 611. 9. What difference is there between a floor 28 feet long by 20 broad, and two others that measure 14 feet a piece by 10; and what do all three come to at $11 per square? Ans. 280 ft. diff. and $94.50. 10. How many planks will floor a room 60 feet long, and 334 wide, supposing the plank 15 feet long, and 15 inches Ans. 1087 nearly. wide? 11. Suppose a house measures, within the walls, 64 feet in length, and 36 feet in breadth, and to be a true pitch, what will it come to roofing at 25s. the square? Ans. 431. 4s. IV. Bricklayers Work is measured by the rod, of 2724 square feet. This work is always computed at the rate of a brick and a fhick, and if the thickness of the wall is more or less, it ust be reduced to that thickness, by the following RULE Multiply the area of the wall in feet, by the number of half bricks in the thickness; divide the product by 8163, and the quotient will be the rods: or, 2. Multiply the area of the wall by the half bricks in the thickness of the wall; the product divided by 3, gives the area in feet, which divide by 2724, the quotient will be the rods required. Note The fraction in rule 1, or in rule 2, commonly rejected in practise. EXAMPLES. 12. How many square rods are there in a wall 523 feet long, 12 feet 9 inches high, 2 bricks thick. Ans. 4r. 27ft. 7in. 13. A gentleman built a wall round his garden, which is 840 feet, and 9 feet high, and 21 brick thick; how many rods doth it contain and what will it come to at $30 per rod? Ans. 46 r. 88 ft. and $1389.709. 14. If each side wall of a building be 45 feet long on the outside, each end wall 15 feet broad on the inside, the height of the building 20 feet and the gable at each end of the wall 6 feet high, the whole being 2 bricks thick: required the content in standard rods? Ans. 12.1761. 15. The end wall of a house is 24 feet in breadth, and 40 feet to the roof; of which is 2 bricks thick, more 13 brick thick, and the rest 1 brick thick: now the gable rises 38 |