Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the side of the regular hexagon be 2 units.
Area Regular hexagon is;
½(12)*(2/(2tan(180/6)))
= 6/tan30
= 6√(3) square units.
Area Shaded is;
Area triangle with height and base 2 units respectively - Are triangle with height (2-√(3)) unit and base 0.28144275258sin45 - Area sector with radius 1 unit and angle 120° + Area triangle with height 1 unit and base sin120 units.
½(2*2) - ½(2-√(3))*0.28144275258sin45 - (120π÷360) + ½(sin120)
= 2 - 0.02666229496 - 1.0471975512 + 0.43301270189
= 1.35915285573 square units.
It implies;
Area Shaded ÷ Area Regular Hexagon to 2 decimal places is;
1.35915285573 ÷ (6√(3))
= 0.13078454452
≈ 0.13
