Brief Description

Students will investigate whether they can expand Hero’s Theorem and Brahmagupta’s Formula to find the area of any convex pentagon/hexagon. They will present their findings in a professional document.

Standards and Frameworks

Technology Standards

6T-P2.  Routinely and ethically use productivity tools, communication tools and research skills to solve a problem.

2M-P2.  Use appropriate technology to display and analyze data.
3M-P6.  Perform mathematical operations on expressions, and solve equations.
4M-P2.  Represent problem situations with geometric models and apply properties of figures.

Academic

At the end of the investigation the students will:

• Know how to use Hero’s Theorem and Brahmagupta’s Formula to find the areas of triangles and quadrilaterals
• Extend the above theorem to pentagons and hexagons.
• Compare the areas of pentagons/hexagons using the original formulas to the areas of the same pentagon/hexagon using the extended formulas.
• Decide if the extended formulas work, explaining why or why not.

• Use the Internet to find Hero’s Theorem and Brahmagupta’s Formula.
• Use the appropriate technology to prepare a professional document to solve whether the theorems can be extended to include pentagons and hexagons.

Students should know:

• how to search using the Internet.
• how to create formulas in Excel.
• how to create  professional documents.

• A computer with Internet access.
• Word, excel or programs that can be used to create professional documents.
• Scanner –useful for scanning diagrams of figures used.

Have students of lower ability work with students of higher ability.

Procedures

Students will work in groups of 4 or 5. They will be given the problem and the assessment criteria in a handout. They will need to find the Theorem’s using the Internet. The group will come up with experimental formulas for the area of a pentagon and hexagon, based on Hero’s and Brahmagupta’s formulas. They will then investigate whether they work by finding the area using their formula and the area of the figures using known formulas. (Students should draw the figures and cut them into triangles and quadrilaterals, so as to work out the exact area).  Students will compare the answers to the exact and experimental areas and come up with a conclusion. They will present their findings in a professional document,  which should include all the details in the assessment below.

Students documents will be assessed for the following:

• Hero’s Theorem and Brahmagupta’s Formulas mentioned.
• Experimental formulas given.
• Diagrams of figures used with construction lines cutting them into quadrilaterals and triangles.
• Results table.
• Conclusion.
• Overall presentation.