Properties of Hexagon and Octagon

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Hexagon:

ABCDEF is a regular hexagon with each side equal to ‘a’ then

▪ Each interior angle = 120 degrees

▪ Each exterior angle = 60 degrees

▪ Sum of all the exterior angles = 360 degrees

▪ Sum of all the interior angles = 720 degrees

▪ Area = $$\frac{3\sqrt{\ 3}}{2}a^2$$.

Octagon: 


ABCDEFGH is a regular octagon with each side equal to ‘x’ then

▪ Each interior angle = 135 degrees

▪ Each exterior angle = 45 degrees

▪ Sum of all the exterior angles = 360 degrees

▪ Sum of all the interior angles = 1080 degrees

▪ Area = $$2\left(1+\sqrt{2}\right)x^2$$

Question 1

ABCDEF is a regular hexagon. What is the ratio of the areas of the hexagon and the rectangle BCEF?

Question 2

Suppose the midpoints of all sides are joined in a regular hexagon to form a smaller hexagon. What is the ratio of the areas of the smaller and original hexagons?

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Properties of Hexagon and Octagon

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