Q1 of 18 Page 167

In the pictures, below, find the difference between the areas of the circle and the polygon, up to two decimal places:

As seen in figure 1,



Diameter of circle = Diagonal of square


∴ Diameter of circle = 4 cm


∴ Radius of circle =


If r = radius of circle


Area of circle = r2 cm2


= 22


= cm2


As seen in figure 2,



Diameter of circle = 4 cm


∴ Radius of circle =


As can be seen from figure 2,


Radius of circle = Side of Hexagon


∴ Side of Hexagon = 2 cm


The regular hexagon is made of 6 equilateral triangles.


Area of polygon (here, regular hexagon) = 6 × Area of triangle


Side of Hexagon = Side of triangle = 2 cm


Area of equilateral triangle = (side)2


= 22


= cm2


Area of polygon (here, regular hexagon) = 6 × Area of triangle


= cm2


∴ Difference between = Area of circle – Area of polygon


Areas


= (4 × π)-(6 × √3)


= (3.14159)-(1.73205)


= 12.56636-10.3923


= 2.17406


≈2.17(upto 2 decimal places).


More from this chapter

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In all the pictures, below, centres of the circles are on the same line. In the first two pictures, the small circles are of the same diameter.


Prove that in all pictures, the perimeters of the large circle is the sum of the perimeters of the small circles.

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