Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Calculating Area R Exactly.
Area R Exactly is;
Area semi circle of radius 2 unit - Area right-angled triangle of height 2√(2+√(2)) unit and width 2√(2-√(2)) unit - Area sector of radius 2 unit and angle 45° + Area isosceles triangle of two equal length, 2 unit each and angle 45° - Area quarter circle of radius 2 unit + Area isosceles right-angled triangle of height and width 2 unit respectively - Area sector of radius 2 unit and angle 22.5°.
It is;
½(4π) - ½((2√(2+√(2)))(2√(2-√(2)))) - ((4π)/8) + ((4√(2))/4) - ((4π)/4) + ½(4) - ((8π)/16)
= 2π - 2√(2) - ½(π) + √(2) - π + 2 - ½(π)
= π - √(2) + 2 - π
= 2 - √(2)
Answer is;
(2-√(2)) square unit.
