Mathematics Question and Solution
Calculating Area Green.
Let x be the radius of the half circle.
a = ½(8)
a = 4 units.
x = (4+b) units.
Recall, x is the radius of the half circle.
c²+4² = (4+b)²
c² = 8b+b²
c = √(8b+b²) units.
d = 2c
d = 2√(8b+b²) units.
e = b+b+d
e = (2b+2√(8b+b²)) units.
e is the side length of the square.
It implies, e is 8 units.
Therefore, calculating b.
2b+2√(8b+b²) = 8
Dividing through by 2.
b+√(8b+b²) = 4
√(8b+b²) = 4-b
8b+b² = (4-b)²
8b+b² = 16-8b+b²
16b = 16
b = 1 unit.
Recall.
x = (4+b) units
And b = 1 unit.
x = 4+1
x = 5 units.
Again, x is the radius of the half circle.
sinf = 4/5
f = asin(4/5)°
g = 2f
g = 2asin(4/5)°
h = 180-g
h = (180-2asin(4/5))
h = 73.7397952917°
sin73.7397952917 = j/5
j = 5sin73.7397952917
j = 4.8 units.
j is the height of the green inscribed triangle.
cos73.7397952917 = k/5
k = 5cos73.7397952917
k = 1.4 units.
k is the base of the green inscribed triangle.
It Implies, Area Green is;
½*j*k
= ½*4.8*1.4
= 2.4*1.4
= 3.36 square units.
