The diameter of the Spacecraft Dimensions Sheet is 9 centimeters, which in turn makes the radius of the circle to be 4.5 centimeters. The width of the rectangle is 3.4 centimeters and the length is 5.1 centimeters. the length of the sides of the octagon will measure 3.4 centimeters, the same as the width of the rectangular side panels.
Students may not be aware of the correct rectangle to measure. It would be hoped that they would realize that the width should be consistent with the length of the sides of the octagon. However, students may question why the top and the bottom rectangle look 'look' different. Explain that this is due to the perspective of the drawing. When a side view of a three dimensional model is shown, the drawing tends to look distorted due to the perspective and the viewing angle.
To make the octagons:
1) With a compass construct a circle with a radius of 4.5 centimeters. Be sure to mark the center. Students should be aware that the sides of the octagon are 3.4 centimeters.
2) Use the ruler to draw a horizontal diameter.
3) Place the compass tip in the center of the circle. Open the compass a little and with the pencil end, mark an arc on both sides of the center of the circle.
4) Open the compass wider (Note: If this step is forgotten, the marks will fail to cross). From each of the arcs, swing the compass to make a large arc on both sides of the diameter. Where the two arcs cross is the point needed to draw the perpendicular diameter.
5) Draw the perpendicular diameter.
6) Place the compass point on the center mark. Construct a small concentric circle.
7) Using one of the angles created, open the compass wider, place the point on the spot where the new circle intersects the diameters. Swing the compass to create a semicircle. Place the point on the other diameter where the little circle meets, and construct another semicircle that intersects the previous one. Where the two semicircles meet will be two points. Connect the two points forming a new diameter (Note: The new diameter will bisect the two angles).
8) Repeat the process in step 7 with the other two angles.
9) Connect the edges of the diameters drawn to construct the inscribed octagon.
10) Students will need to construct two octagons for the pattern.
Constructing the rectangles:
11) The eight rectangles need to be 3.4 centimeters by 5.1 centimeters . Some students may need to use the corner of the sheet of the paper as the first two sides, and they can measure for the other two sides. The more advanced students can use perpendicular bisectors to construct parallel sides, and then they can do their measurements.
Note: If the pattern is being constructed entirely by hand, the given scale dimensions will fit on an 8 1/2 x 11 sheet of paper. The students will need to determine the lay-out of the pattern.
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