Mathematics Question and Solution
Calculating Area Shaded.
Let r be the radius of the semi circle.
Calculating r.
((6r/√(10))-2)²=(r/2)²+(3r/2)²
72r²-48√(10)r+80=50r²
22r²-48√(10)r+80= 0
11r²-2⁴√(10)r+40= 0
Therefore;
r ≠ 0.57496 cm.
r = 6.32455 cm.
The height, h of the shaded triangle is;
h = r/2 cm.
The base of the shaded triangle is;
b = 2r cm.
And r = 6.32455 cm.
Therefore;
h = 6.32455/2
h = 3.162275 cm.
And
b = 2(6.32455)
b = 12.6491 cm.
It implies;
Area shaded triangle is,
½(bh)
= ½(12.6491*3.162275)
= ½(39.9999327025)
= 19.9999663513 cm²
= 20 cm²
