Mathematics Question and Solution
8² = 2a²
a² = 32
a = √(32)
a = 4√(2) units.
a is the side length of the square.
c = a+b
c = (4√(2)+b)
c is the diameter of the circle.
d = ½(c)
d = ½(4√(2)+b) units.
d is the radius of the circle.
e = d-b
e = ½(4√(2)+b)-b
e = ½(4√(2)+b-2b)
e = ½(4√(2)-b) units.
f = ½(a)
f = 2√(2) units.
Calculating b.
(½(4√(2)+b))² = (2√(2))²+(½(4√(2)-b))²
¼(32+8√(2)b+b²) = 8+¼(32-8√(2)b+b²)
32+8√(2)b+b² = 32+32-8√(2)b+b²
16√(2)b = 32
√(2)b = 2
b = 2/√(2)
b = √(2) units.
Recall.
d = ½(4√(2)+b)
And b = √(2) units.
d = ½(4√(2)+√(2))
d = ½(5√(2)) units.
Again, d is the radius of the circle.
Area circle is;
πd²
= π(½(5√(2)))²
= π(¼*50)
= ½(25π) square units.
= 39.2699081699 square units.
