Investigating the Area of Polygons

•Area of triangles•Angles inside polygons•Geometric reasoning

•Surds•Simplifying algebra

•Pythagoras•Trigonometry

Find the areas

HINT: Split into equilateral triangles HINT: draw a square around the outsideClick for hint 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

Solutions – video hereHexagon₌ 24√3₌ 41.569…₌ 41.6 cm2 (3sf)

Octagon₌ 32(√2 + 1)₌ 77.254…₌ 77.3 cm2 (3sf)

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 polygonClick for extension

Find the area of a regular hexagon with sides n cm

Find the area of a regular octagon with sides n cm

Solutions - video here

Hexagon₌ 3√3n2/2

How would you explain your proof? Can you make a video explaining it?

Octagon₌ 2n2(√2 + 1)

Does this work with your answer for n=4? What skills did you use?

How about a general formula

Hint: split any regular polygon into triangles. How can you find the

height? SOHCAHTOA…

Solutions and more info here

Thanks!

Created by Emma Morgan www.mrsmorganmaths.weebly.com@em0rgan