Mathematics Question and Solution
Calculating the area of the red rectangle.
Let a be the radius of the half circle.
b = ½(a) units.
Calculating a.
a² = (½(a))²+1²
a² = ¼(a²)+1
(3/4)a² = 1
a² = 4/3
a = √(4/3)
a = ⅓(2√(3)) units.
a = 1.1547005384 units.
Again, a is the radius of the half circle and also the width of the red rectangle.
Notice!
b = ½(a)
b = ½(1.1547005384)
b = 0.5773502692 units.
c = a+b
c = 1.7320508076 units.
c = √(3) units.
c is the length of the red rectangle.
Therefore, area red rectangle is;
a*c
= ⅓(2√(3))*√(3)
= ⅓*2*3
= 2 square units.
