Mathematics Question and Solution
Red area is;
½(Area rectangle of length 2r and width r - area semi circle of radius r) - area triangle of height 2r and base r + area sector of radius r and angle (2tan–¹(1/2))° + area triangle of two equal length r, and angle (180-2tan–¹(1/2))°, the angle they form.
Therefore;
½(2r²-½(πr²))-r²+((2tan–¹(1/2))*(πr²)÷360)+½(r²sin(180-2tan–¹(1/2))
= r²-¼(πr²)-r²+0.14758361765πr²+0.4r²
= 0.4r²+0.14758361765πr²-0.25πr²
= 0.4r²−0.1024163824πr²
= r²(0.4−0.3217505546)
= (0.0782494454)r² square units.
