TASKS

Tasks

Name of Writer

Name of Institution

Task 1.2.4a (The 9 - pin geoboard)

Quadrilaterals

The numbers of quadrilaterals that can be obtained through 9 - pin geoboard are as follows:

(Note: Explanation, Areas and Perimeters are in Appendix)

There are 16 different shapes that can be obtained from the 9 - pin geoboard. It has been taken under consideration that repeated shapes and structures are avoided because similar structures do not add any different shape in the construction of shapes. The similar shapes mean the following shapes:

No one can simply analyze that these are not the different shapes in one is the copy of another but the only difference is that one shape has been mirror image of the other.

Explanation and Working

The reason for concluding the fact that there will be no more than 16 quadrilaterals drawn in a 9 - pin geoboard is that quadrilaterals needs four sides to be drawn and in a 9 - pin geoboard the formula for possible quadrilaterals is 2n i.e. 24 = 16, where 'n' are the sides of the structure . It is explained above that congruent triangles are not considered because they are not a new quadrilateral they are just the transformation and reflection of the other quadrilateral.

Triangles

The numbers of triangles that can be obtained through 9 - pin geoboard are as follows:

There are 8 different shapes of triangles that can be obtained from the 9 - pin geoboard. It has been taken under consideration that repeated shapes and structures are avoided because similar structures do not add any different shape in the construction of shapes. The similar shapes criteria have been discussed above which only change the axis and not the shape of the structure.

Explanation and Working

The reason for concluding the fact that there will be no more than 8 trianlges drawn in a 9 - pin geoboard is that triangle needs four sides to be drawn and in a 9 - pin geoboard the formula for possible triangles is 2n i.e. 23 = 8, where 'n' are the sides of the structure. It is explained above that congruent triangles are not considered because they are not a new quadrilateral they are just the transformation and reflection of the other quadrilateral.

Task 1.2.4b (The 9 - pin geoboard Areas)

The structures obtained in the first task are certainly different from each other. Though they all are of same shapes but the differences in area varies with the change in the structure of the quadrilateral. We can analyze that the first structure i.e. square has the largest area among all the quadrilateral shapes because it covers all the 9 - pin geoboards. There is a variation in the areas are observed as long as there is a change in the size and shape of the quadrilateral. The smallest of the area among all the structures is the area of the last shape which is a square because it covers the least number of pins of geoboards. It can be noticed throughout the 9 - pin geoboard analyses ...