Mathematics Question and Solution
Calculating Required Shaded Area.
Notice.
The three circles are congruent.
Therefore, the required shaded area is;
Area equilateral triangle with side r units+3(area sector with radius r units and angle 60° - area regular triangle with height r units and base rsin60 units).
= 0.5r²sin60+3((60π*r²/360)-(0.5r²sin60))
= ¼√(3)r²+3(⅙(πr²)-¼√(3)r²)
= ¼√(3)r²+½(πr²)-¾√(3)r²
= ½(πr²)-½√(3)r²
= ½(π-√(3))r² square units.
