Friday, August 1, 2014

Drawing Polygons using Pro-Bot given Area or Perimeter

In this programming assignment, we shall draw polygons using Pro-Bot, given the area or perimeter of the polygons. Your first task is to figure out the dimensions of the polygons from the given data and your second task is to write programs to draw the polygons using Pro-Bot. You can use either sequential programming or Repeat loops to draw the polygons, depending on whether they are irregular or regular.

Computer Science concepts involved:  Sequential programming, Repeat loops

Math concepts involved:  Polygons (regular and irregular), Area, Perimeter, Measurement, Angles

Hours required: 3 - 4

Draw Polygons using Pro-Bot given the perimeter:

1. The perimeter of a regular, 4 sided polygon is 32 cm. The interior angles are all 90 degrees each. Can you write a program for Pro-Bot to draw this polygon? What kind of a polygon is it?
2. The perimeter of a regular, 4 sided polygon is 32 cm. A pair of opposite interior angles are 60 degrees each. Can you write a program for Pro-Bot to draw this polygon? What kind of a polygon is it?
3. The perimeter of a regular 3 sided polygon is 18 cm. The interior angles are all 60 degrees each. Can you write a program for Pro-Bot to draw this polygon? What kind of a polygon is it?
4. The perimeter of a 3 sided polygon is 24 cm. The interior angle between the shortest sides is 90 degrees. The interior angle between the shortest and longest sides is 54 degrees. The sum of the lengths of the shortest sides is 14 cm. The difference between the lengths of the shortest sides is 2 cm. What kind of a polygon is it? Can you write a program for Pro-Bot to draw this polygon?
5. The perimeter of a 4 sided polygon is 24 cm. Two of its sides are parallel to each other and the other two are not. The sides that are not parallel are equal in length. Both the angles coming from a parallel side are equal: the pair of angles coming from the longer parallel side is 54 degrees each and the pair of angles coming from the shorter parallel side is 126 degrees each. The sum of the lengths of the parallel sides is 14 cm. The shorter of the parallel sides is 4 cm. Can you identify the polygon? Can you write a program for Pro-Bot to draw this polygon?
6. The perimeter of a 4 sided polygon is 24 cm. Both sets of opposite sides are parallel. What kind of a polygon do you think it is? The ratio of the shorter side to the longer side of this polygon is 1/2; i.e.; each shorter side is half the length of the longer side. One pair of interior opposite angles is 60 degrees and the other pair of interior opposite angles is 120 degrees. Can you write a program for Pro-Bot to draw this polygon?
7. The perimeter of a 5 sided regular polygon is 25 cm. Can you write a program for Pro-Bot to draw this polygon? What kind of a polygon is it? What is the value of each interior angle?

Drawing Polygons using Pro-Bot given the area:

1. The area of a regular, 4 sided polygon is 24 square cm. The interior angles are all 90 degrees each. Can you write a program for Pro-Bot to draw this polygon? What kind of a polygon is it?
2. The area of a 4 sided polygon is 24 square cm. The opposite sides are equal in length and the interior angles are all 90 degrees each. The longer side measures 2 cm more than the shorter side. The sum of the lengths of the long side and the short side is 10 cm. Can you write a program for ProBot to draw this polygon? What kind of a polygon is it?
3. The area of a 3 sided polygon is 24 square cm. The interior angle between the shortest sides is 90 degrees. The interior angle between the shortest and longest sides is 54 degrees. The sum of the lengths of the shortest sides is 14 cm. The difference between the lengths of the shortest sides is 2 cm. What kind of a polygon is it? Can you write a program for ProBot to draw this polygon?
4. The area of a 4 sided polygon is 24 square cm. Both sets of opposite sides are parallel to each other. What kind of a polygon is it? The distance between the longer parallel sides is 4 cm. The perimeter of this polygon is 20 cm. One pair of interior opposite angles is 60 degrees and the other pair of interior opposite angles is 120 degrees. Can you write a program for ProBot to draw this polygon?