Question

Centred at each corner of a regular hexagon, a part of a circle is drawn and a figure is cut out as shown below:
Kerala Syllabus 9th Standard Maths Solutions Chapter 9 Circle Measures 336
what is the area of this figure?
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Answer 1

Answer:

4.1 cm² (approx.)

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Step-by-step explanation:

On observing the figure, we notice that the radius of the part of the circle in hexagon is 1 cm.

∵ Each side of hexagon = 2 cm

A regular hexagon has interior angle = 120°

Thus, the angle subtended by the sector of the circle on its center is 120°

Area of sector of a circle =  $\frac{\theta}{360} \: *\: r^{2}$

= $\frac{120}{360} \: *\: 1^{2}$

= 22/ 21 cm²

There are 6 such circles

Therefore,  area = 6 × $\frac{22}{21}$

= 2 × 22/ 7

= 44/ 7

= 6. 3 cm²(approx.)

Area of hexagon = (3√3 a²)/ 2

here a is the side of the hexagon

= (3√3 × 2²)/ 2

= 6√3

= 10.4 cm² (approx.)

Area of the figure = Area of hexagon - Area of circles

= 10.4 - 6. 3

= 4. 1 cm²