Q3 of 18 Page 157

Calculate perimeter of a regular hexagon with vertices on a circle of diameter 1 centimetre.

The figure is shown below:



Diameter of circle, CF = 1 centimetre


∴ Radius of circle = cm = 0.5 cm


As can be seen from figure,


Radius of circle = Side of Hexagon


∴ Side of Hexagon = 0.5 cm


Perimeter of Hexagon = 6 × Side of Hexagon


= 6 × 0.5


= 3 cm


More from this chapter

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1

Prove that the circumcentre of an equilateral triangle is the same as its centroid.

i) Calculate the length of side of an equilateral triangle with vertices on a circle of diameter 1 centimetre.


ii) Calculate the perimeter of such a triangle.

 2

Calculate the perimeter of a square with vertices on a circle of diameter 1 centimetre.

 1

The perimeter of a regular hexagon with vertices on a circle is 24 centimetres.

i) What is the perimeter of a square with vertices on this circle?


ii) What is the perimeter of a square with vertices on a circle of double the diameter?


iii) What is the perimeter of an equilateral triangle with vertices on a circle of half the diameter of the first circle?

 2

A wire was bent into a circle of diameter 4 centimetres. What would be the diameter of a circle made by bending a wire of half the length?