WORKBOOK SAMPLER Chapter 7: Polygons - Nelson Education

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7.5 Applications of Polygons You will need • a millimetre ruler • a protractor • a compass Try These Look around your classroom. i) Where do you see a polygon Name this polygon. e.g., The top of my desk is a rectangle. ii) Describe some properties of this polygon. e.g., It has two pairs of equal sides. The equal sides are parallel. All four interior angles are right angles. Angela creates designs with floor tiles. To cover a floor with no gaps, the tiles must fit together so that the angle measures have a sum of 3608. Create a design that Angela could use. 360° 1 Draw a design that could be made with floor tiles. Use at least two different polygons. The polygons must fit together so that the angle measures have a sum of 3608. Record angle measures with a sum of 3608. e.g., 120° 90° 60°45° 45° 120° 60° 45° 45° 75° 90° 120° 90° 75° Example Jordan is a machinist in Yellowknife. This chart shows a method he uses to space bolt holes at equal distances around a circle. How can Jordan use a regular pentagon to space five holes at equal distances around a wheel To get this many holes around a circle … … multiply the diameter of the circle by the number below. The result is the side length of a regular polygon with vertices at the locations of the holes. 3 0.8660 4 0.7071 5 0.5878 6 0.5000 8 0.3827 10 0.3080 12 0.2588 178 Apprenticeship and Workplace 12 NEL 22 Apprenticeship and Workplace 12 NEL
Solution A. Use a compass to construct a circle. What is the diameter of your circle e.g., 24 mm The diameter of the circle is mm. B. Use the chart. Multiply the diameter by the number for five holes. The product is the side length of a regular pentagon. ( e.g., 40 mm)(0.5878) 5 e.g., 23.512 mm The side length is e.g., 24 e.g., 40 mm. ReflecTinG The measurements in this example are given in millimetres. When would a machinist have to measure much more precisely Practice 1. A machinist wants to space eight bolt holes at equal distances around a wheel. The diameter of the wheel is 60 cm. a) What regular polygon can the machinist use to locate the holes regular octagon b) How long will the sides of the polygon be, to the nearest millimetre (60 cm)(0.3827) 5 22.962 cm The sides of the polygon will be about 230 mm long. Hint Use the charts inside the back cover for converting units. 2. Elaine is looking at floor-tile designs. Each design is made by repeating a regular polygon. The polygon in each design is different. a) What is one regular polygon that could be used to make a floor-tile design Explain. e.g., A square; the interior angle is 908, and (4)(908) 5 3608. b) What is one regular polygon that could not make a tiling design Explain. e.g., A regular octagon; the interior angle is 1358. Regular octagons do not fit together so that the sum of the angle measures is 3608. NEL NEL Chapter 7 Polygons 179 Chapter 7 Polygons 23
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WORKBOOK SAMPLER Chapter 7: Polygons - Nelson Education

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