7. (a) What do we call such a statement? (b) Does this statement hold true for all rectangles? 8. (a) Measure your desk, your book, and your school room and find their areas. (b) What units will you use for measuring each of these? 9. (a) In what kind of rectangle is the length equal to the width? (b) If e stands for the edge of a cube, we may say, area of one surface or = edge x edge, 10. If the edge of a cube is 3 inches, then 11. Find the area of a face if the edge of cube is 6 in.; 4 in. II. Surface of Cube and Oblong 1. Imagine the surface of the cube as being a very thin covering that may be peeled off as an onion skin. Run a knife down one edge and peel off that face without detaching it. Do the same for the opposite face. Then peel off the rest in one piece. Make a pattern of this surface on stiff paper. Put on necessary flaps, cut out, paste, and put together. 2. Do the same for the oblong. 3. Another name for this oblong is parallelopiped. A cube is also a parallelopiped, but all of its edges are equal. 4. Make two patterns, one for an oblong with square bases and one with rectangular bases. 5. (a) How many faces has a cube? (b) How do the different faces compare in size and shape? (c) How would you find the total surface, that is, the sum of the areas of all of the faces? (d) The total surface of cube = 6 x area of one face. For cube, Tot. S = 6 e2 6. How many faces of a cube are lateral faces? Can you see the reason for the following formula? For cube, Lat. S = 4 e2 7. (a) How many different dimensions has the first oblong, A? the second, B? (b) Name them. (c) What is the shape of the pattern of the lateral surface? (d) What is the total length of this rectangle? (e) What dimension of the oblong is the width of this rectangle? (f) The formula for the lateral surface is (g) Put this formula into a complete English sentence and see if it is true for both figures. (h) Can you think of a practical problem in which you would want to find the lateral area only? Would the painting of a fence be such a problem? (i) How many bases has an oblong? (j) How can you find the area of each? (k) How can you find the total area of the parallelopiped? (1) Lat. S=2.(1+w) h or Lat. S 2 h(l+w) = 8. Find the total area of a chest if its length is 10 ft., its width 4 ft., and its height 3 ft. Show why this formula is correct. 10. The second method is more convenient when only the total area is desired. If the area of the lateral surface and one base only is required, the first method is the better. 11. A flower box is 8 ft. long, 10 in. wide, and 8 in. high, inside measurement. How many square feet of tin will be required to line the box? No allowance is made for waste. 12. How many square yards of cement pavement are needed for a walk 4 ft. wide in front of a lot 50 ft. wide? 13. (a) An athletic field is inclosed by a board fence 10 ft. high. The field is 600 ft. x 400 ft. One gallon of paint covers 250 sq. ft. with two coats. How many gallons will be needed to paint the fence? (b) A painter calls 100 square feet a square. If he can paint a square of fence in one hour, what will be the cost of labor in painting the fence? Inquire of a painter the scale of wages. (c) What will be the total cost? 14. (a) How many square feet are in the side walls of your school room? (b) Find their area with the doors and windows taken out. 15. (a) A house is 40 ft. x 32 ft. x 18 ft. How many squares in its surface? (Use the nearest integer.) (b) Allow 14 squares for the dormer windows, cornice, and porch. How many gallons of paint are needed? (No allowance is made for doors and (c) Find the cost of the paint at $4.25 per gal. hour. Find the total cost. (e) How many days are needed for the work? D. SQUARE ROOT I. Study of Numbers and Factors 1. (a) On squared paper draw a square inclosing 9 sq. 3. The factors of a number are other numbers which, multiplied together, produce the given number. 4. A prime number can be exactly divided only by itself and one. |