This task sheet contains geometry tasks that were inspired from the pattern of the mosaic 'The Three Graces'. They are accompanied by the solutions that the students managed to find working in their transnational teams. They worked on the tasks, uploaded them again on the platform and so they all made changes and/or improvements to the other students' work up to then.

 

Activity 1

If each circle has radius equal to R cm, find in terms of the R:

A. The total area of the leaves.

B. The total area of the red curvilinear rhombus

 

 

 

 

 

 

 

Solution A

Each leave is a intersection area of two circles

 

 

 

 

 

 

 

and is composed from two sections of circles:

 

 

 

 

 

 

The area of each section of circle is equal to: The area of sector of circle minus the area of the triangle.

The sector of circle is a quadrant and the triangle is isosceles and orthogonal.

So, the area of each section of circle is:

The area of each leave is equal with twice a area of  the section of circle:  

           

And finally the total area of leaves is

         

Solution B

The area of each of the red curvilinear rhombus is equal t o:

The area of circle minus the area of four leaves.

So, is