Question

In the adjoining figure ABCDEF is a regular hexagon. If the radius of the circle is 14 cm, then find the area of the shaded region. ​

Answer 1

Answer:

205.33

Step-by-step explanation:

it's a regular hexagon with radius 14

so angle made by each side at centre that is AOB =360/6= 60

so we know the angle and radius so we can find the sector area and segment area as well

and more clearly radius are dividing the hexagon into six equilateral triangles

so area of equilateral triangle = (√3)/4*a^2

so area of parallelogram in the given figure

= 2*(√3/4)*14*14=98√3

and two segments area we need to find

sector area = (¤/360)*πr^2

= (1/6)*(22/7)*14*14

=308/3

from that we need to take out the triangle area

=308/3 - 49√3

= 17.79

so there are two segments so area = 2*17.79= 35.59

so shaded area = 35.59+98√3= 205.33