Mathematics Question and Solution
Calculating p.
2² = (½(3p)+p)²+(½(p))²
4 = (5p/2)²+(p/2)²
4 = (25p²/4)+(p²/4)
4 = ¼(26p²)
16 = 26p²
p = √(16/26)
p = √(8/13) units.
p = 0.7844645406 units.
It implies;
a = ½(3p)
a = 0.5*3*0.7844645406
a = 1.1766968108 units.
a is the radius of the bigger semi circle.
b = ½(p)
b = 0.5*0.7844645406
b = 0.3922322703 units.
b is the radius of the two congruent semi circles.
c = p
c = 0.7844645406 units.
c is the radius of the quarter circle.
Therefore, shaded area is;
Area semi circle with radius 1.1766968108 units + Area circle with radius 0.3922322703 units + Area quarter circle with radius 0.7844645406 units.
= ½(1.1766968108)²π+(0.3922322703)²π+¼(0.7844645406)²π
= 2.1749487604+0.4833219468+0.4833219468
= 3.1415926539 square units.
= π square units.
