1. With a ladder whose foot was placed 14 ft. from a burning building the firemen were able to rescue a child at a window 48 ft. from the ground. How long was the ladder? 2. A 25-ft. ladder whose foot is 7 ft. from the base of the building just reaches the top of a flat-roofed building. How high is the building? 3. Mrs. Chase has a triangular flower bed in a corner of her rectangular house lot. The two short sides of the bed are 12 ft. and 16 ft. At 21 a foot, how much will it cost for wire netting for the third side? 4. A right-angled triangle has two equal sides; its hypotenuse is 16 in. Find the length of one of the other 5. How many acres in a square field whose diagonal is 64 rd. ? 6. Mr. Blake has a square field of 2 A. dimensions? What are its 7. A rectangular field 90 rd. by 48 rd. is separated into two parts by a path running diagonally through it. Find the length of the path. Find the number of acres in each part. 8. Arthur lives 48 rd. east of the schoolhouse, and Fred 55 rd. south of it. Arthur and Fred live how far apart? 9. How long a throw is it from the home plate to second base on a baseball field 90 ft. square? 10. The base of an isosceles triangle is 16 ft. and each of the other sides 17 ft. Find the altitude. 11. What is the altitude of an equilateral triangle each of whose sides is 20 ft? 12. In going from one corner to the opposite corner of a field 56 rd. by 33 rd., how much is saved by going diagonally across the field? 13. The pole of a circus tent is held in place by ropes 111 ft. long running from the top of the pole to stakes 105 ft. from the base of the pole. How high is the pole? 14. The guy ropes of a derrick 28 ft. high are fastened to the ground 45 ft. from the foot of the derrick. How long are the ropes ? 15. A tree broken 12 ft. from the ground, but not detached, fell so that its top struck the ground 35 ft. from the foot of the tree. How high was the tree? REVIEW OF MENSURATION TRIANGLES Oral 1. What is a triangle? 2. Draw and describe a right-angled triangle. An acute-angled triangle. An obtuse-angled triangle. 3. Draw and describe an equilateral triangle. An isosceles triangle. A scalene triangle. 4. What is the altitude of a triangle? 5. How is the area of a triangle found? 6. What is the area of a triangle whose base is 61 ft. and whose altitude is 8 ft.? 7. What is the altitude of a triangle whose base is 5 in, and whose area is 40 sq. in. ? 8. The perimeter of an isosceles triangle is 20 in.; its base is 6 in. How long is each of the other sides? QUADRILATERALS 1. What is a quadrilateral? 2. Tell what name is given to quadrilaterals having (1) two pairs of parallel sides. (2) one pair of parallel sides. (3) no two sides parallel. 3. Describe a rectangle. rhombus. Oral A A square. A rhomboid. A 4. How is the area of a parallelogram found? A trape zoid? A trapezium? 5. A window pane is 15 in. by 30 in. What is the lighting surface? Express its perimeter in feet. 6. The area of the top of a rectangular table is 10 sq. ft.; its width is 21 ft. Find its length. Its perimeter. 7. The parallel sides of a trapezoid, 8 in. and 12 in.. respectively, are 6 in. apart. Find the area of the trapezoid. WRITTEN PROBLEMS 1. How many acres in this field? 2. A rectangular field of equal area is 12 rd. wide. How long? 3. What are the dimensions of a square field of equal area? 16 rd. 20 rd. 30 rd. 4. The base of a triangular field of equal area is 40 rd. What is its altitude? 5. A man has two fields of trapezoidal shape, the altitude of each being 20 rd. The parallel sides of one are 60 rd. and 20 rd. The parallel sides of the other are 50 rd. and 30 rd. Find the number of acres in each field. 6. The diagonal of a trapezium is 36 ft., and the two perpendiculars from the angles opposite the diagonal are 19 ft. and 27 ft., respectively. What is the area of the trapezium? 1. What is a circle? CIRCLES 2. Define radius. Diameter. Circumference. Oral The ratio of the circumference to the diameter, 3.1416, is expressed by the symbol π, called pi (pī). 3. When c represents the circumference, the radius, d the diameter, and a the area, explain these statements: 1 in. 4. Find the area of a circle 1 in. in diameter; of a 1 in. square 1 in. long. By comparing the area of the circle with the area of the square the area of the circle is found to be .7854 of the area of the square. Hence, the area of any circle may be found by multiplying the square of its diameter by .7854. This may be ex ressed as follows: a = d2 x .7854. For approximate estimates T is regarded as 34; .7854 vis ff. WRITTEN PROBLEMS Find, approximately : 1. The length of the tire of a wheel 42 in. in diameter. 2. The diameter of a water main 44 in. in circumference. 3. The area of a circular window 171⁄2 in. in diameter. 4. The area covered in one revolution by a steam ad roller 35 in. in diameter and 56 in. wide. 5. The capacity of a baking powder tin 1 in. in diameter and 7 in. high. 6. A restaurant coffee tank 15 in. in diameter and 22 in. high is half full. Find the number of gallons of coffee. 7. The convex surface of the tank in Problem 6 is of aickel. Find its area. 8. The front wheels of a wagon are 42 in. in diameter. The spokes of the hind wheels are 7 in. longer than the |