APPENDIX. APPLICATIONS. PROBLEM I. RIGHT-ANGLED TRIANGLES. 1. In a right-angled triangle having the base 40 feet, the perpendicular 9 feet, to find the hypotenuse. (B. V. Prop. VII.) the square of the base, the Square feet. square of the perpendicular, the square of the hypotenuse, 1681 Ans. therefore the hypotenuse 41 feet. 2. Having the base 3 feet, the perpendicular 4 feet, Ans. 5 feet. to find the hypotenuse. 3. Having the base 8 yards, and the perpendicular 6 Ans. 10 yards. 4. Having the hypotenuse 61 feet, the perpendicular yards, to find the hypotenuse. Ans. therefore the base 60 feet. 5. Having the hypotenuse 15 feet, the base 9 feet, to find the perpendicular. Ans. 12 feet. 6. Having the hypotenuse 25 feet, the base 7 feet, to find the perpendicular. Ans. 24 feet. 7. Having the hypotenuse 85 feet, the perpendicular 84 feet, to find the base. Ans. 13 feet. PROBLEM II. (B. V. PROPS. I. AND II.) Area of square, rectangle, or parallelogram. 1. What is the area of a rectangle, whose length is 11 feet and breadth 13 feet? 13 multiplied by 11 is= Ans. 143 sq. ft. 2. What is the area of a square, whose side is 61⁄2 feet? 6 reduced to decimals is 6.5; and 6.5 multiplied by 6.5 is Ans. 42.25 sq. ft. 3. What is the area of a square, whose side is 204.3 feet? Ans. 41738.49 sq. ft. 4. What is the contents, in square yards, of a rectangle whose base is 66.6 feet, and altitude 33.3 feet? Reduce the feet to yards, and multiply. Ans. 246.42. 5. Find the area of a rectangular board, whose length is 12 feet, and breadth 9 inches, or foot. Reduce the fractions to decimals. Ans. 9.375 sq. ft. 6. Find the number of square feet of painting in a parallelogram whose base is 37 feet, and whose altitude is 5 feet. Ans. 194.25. 7. Find the number of square yards in a floor, whose length is 5.33 yds. and breadth 4.25 yds. Ans. 22.6525. PROBLEM III. (B. V. PROP. III. COR. IV.) 1. Find the area of a triangle, whose base is 625 feet, and altitude 520 feet. Ans. 162500 sq. ft. 2. Find the number of square yards in a triangle, whose base is 40 feet and altitude 30 feet. Find the number of square feet, and then divide by 9, the number of square feet in a square yard. Ans. 66. 3. Find the number of square yards in a triangle, whose base is 49 feet and altitude 25 feet. Ans. 68.7361. PROBLEM IV. (B. V. PROP. VI.) In a trapezoid, the parallel sides 750 feet and 1225 feet, and the perpendicular distance between them 1540 feet, what is the area? Ans. 1520750 sq. ft. 2. How many square feet are contained in a plank, whose length is 12 feet, breadth at the greater end 15 inches, and at the less end 11 inches? Ans. 13.541. 3. How many square yards in a trapezoid, whose parallel sides are 240 feet, 320 feet, and altitude 66 feet? Ans. 2053.33. PROBLEM V. (B. VII. PROP. VIII. SCH. I.) To find the circumference of a circle when the radius is known. is 12? 1. What is the circumference of a circle whose radius Ans. 78.54. 2. If the diameter of the earth is 7921 miles, what is the circumference? Ans. 24884.6136. 3. What is the diameter of a circle whose circumference is 11652.1944 ? Divide the circumference by 3.1416. Ans. 37.09. 4. What is the diameter of a circle whose circumference is 6850 ? Ans. 2180.41. PROBLEM VI. (B. V. III. PROP. VI. COR., AND PROP. VIII. SCH. II.) To find the area of a circle. 1. Find the area of a circle whose diameter is 10, and circumference 31.416. Ans. 78.54. |