1. Investigating the Area of Polygons Area of triangles Angles inside polygons Geometric reasoning Surds Simplifying algebra Pythagoras Trigonometry

2. Find the areas HINT: Split into equilateral triangles HINT: draw a square around the outside Click for hint Extension: Find the area of a regular pentagon, with sides of 4cm. What hint might you give to help someone find the area of a pentagon? Click for extension

3. Solutions – video herehere Hexagon ₌24√3 ₌41.569… ₌41.6 cm 2 (3sf) Octagon ₌32(√2 + 1) ₌77.254… ₌77.3 cm 2 (3sf)

4. What about a general formula? HINT: Split into equilateral triangles HINT: draw a square around the outside Extension: How about a general formula? This will require some trigonometry. Try using a similar method as the hexagon, but consider how to find the internal angle in a regular polygon Click for extension Find the area of a regular hexagon with sides n cm Find the area of a regular octagon with sides n cm

5. Solutions - video herevideo here Hexagon ₌3√3n 2 /2 How would you explain your proof? Can you make a video explaining it? Octagon ₌2n 2 (√2 + 1) Does this work with your answer for n=4? What skills did you use?

6. How about a general formula Hint: split any regular polygon into triangles. How can you find the height? SOHCAHTOA… Solutions and more info herehere

7. Thanks! Created by Emma Morgan www.mrsmorganmaths.weebly.com www.mrsmorganmaths.weebly.com @em0rgan