Mathematics Question and Solution
Calculating Area Shaded.
Let r be the radius of the ascribed half circle.
Therefore;
½(r) is the radius of the inscribed circle and also the height of the shaded area.
a = r+½(r)
a = ½(3r) cm.
tanb = (½(r))/(3r/2)
tanb = 1/3
b = atan(⅓)°
sinb = c/2r
sin(atan(⅓)) = c/2r
0.31622776602 = c/2r
c = 0.63245553203r cm.
cosb = d/2r
cos(atan(⅓)) = d/2r
d = 1.8973665961r cm.
e = d-2
e = (1.8973665961r-2) cm.
Calculating r.
sin(atan(⅓)) = 0.5r/(1.8973665961r-2)
0.6r-0.63245553203 = 0.5r
0.1r = 0.63245553203
⅒(r) = 0.63245553203
r = 6.3245553203 cm.
Again, r is the radius of the ascribed half circle.
Recall.
½(r) is the radius of the inscribed circle and also the height of the shaded area.
Let f = ½(r) cm.
And r = 6.3245553203 cm.
f = ½(6.3245553203)
f = 3.16227766017 cm.
g = 2r
And r = 6.3245553203 cm.
g = 2*6.3245553203
g = 12.6491106406 cm.
g is the diameter of the ascribed half circle.
Shaded Area is;
½*f*g
= 0.5*3.16227766017*12.6491106406
= 20 cm²
