Given The Width Of A Hexagon, To Find The Side. (Fig. 66.)

S = side of hexagon.

Method 1. Draw the line ab = given width of the hexagon. Erect an indefinite perpendicular, ac, from a.

Let 12 Bl. rest at b; 6 11/12 To. on ab. Continue line of Bl. to ac. Mark intersection, d. Apply Formula 5.

Formula 5. S = ad.

Method 2. Bisect the line ab and erect an indefinite perpendicular; use the square as in method 1. The intersection of the line bd with the perpendicular = S.

Suggestive Exercises

31. What are the dimensions of the blade and the tongue of the standard steel square ? Into what fractional parts of an inch is each edge? of a square divided? Which is the face side of the square? What is the length of the blade upon the scale of 1" to 1'? Of the tongue? Lay off 18' 9", using the 1" scale; 21' 6"; 9' 7". Demonstrate the use of the board measure. How many feet are there in a board 16' long, and 11" wide ? 18' long, 22" wide ? Demonstrate the use of the brace measure. The use of the diagonal scale.

Fig. 66. - Given the Width of a Hexagon to find the Side.

32. What are the accessories for working out steel square problems ?

33. Demonstrate the use of the steel square in dividing a board into any number of equal parts.

34. Demonstrate the method of finding the number of degrees in each angle of a regular polygon. Of finding the degrees in the miter of a polygon. What is always the sum of the two angles with the hypotenuse of a right angle triangle ? What are the symbols of the blade and the tongue ? Demonstrate the method of finding the figures upon the square which will give the angles and miters of a polygon.

Construct by this method an equilateral triangle; a rectangle; a hexagon; an octagon. What tool is a convenience in marking duplicate angles?

35. Demonstrate the method of bisecting an angle with a steel square.

36. Demonstrate the method of finding the center of a circle which will pass through three given points

37. Demonstrate the method of finding the greatest square which can be contained within a given circle.

38. Demonstrate the method of finding a square one half the area of a given square. Demonstrate the method of finding a square twice the area of a given square.

39. Demonstrate the method of constructing a circle equal in area to two given circles. How may the problem be applied to any number of circles?

40. Demonstrate the use of the octagon scale. What figures upon the side of a square will give the width of the side of an octagon ? Demonstrate its use. What other tool may be used in the same way ? Demonstrate the method of finding the sides of an octagon from the diagonals of a square.

41. Demonstrate the method of finding from a given side the width of an octagon. What previously given method may be reversed to give the same results ?

42. Demonstrate the method of finding from a given side the width of a hexagon.

43. Demonstrate the method of finding the diagonal of an octagon from its given side.

44. Given the side of a hexagon, demonstrate the method of finding its diagonal.

45. Given the width of an octagon, demonstrate the method of finding the length of the side. By what other previously described method may the problem be solved ?

46. Given the width of a hexagon, demonstrate two methods of finding the length of the side.