Mathematics Question and Solution
Calculating The Required Shaded Area.
Let it be x.
a² = 1²+0.5²
a = √(1.25) units.
b = 2a
b = 2√(1.25) units.
tanc = 1/0.5
c = atan(2)°
tan(atan(2)) = d/√(1.25)
2 = d/√(1.25)
d = 2√(1.25) units.
(e/sin45) = (2√(1.25)/sin(180-45-atan(0.5)))
e = 1.79505493571 units.
f = e-1
f = 0.79505493571 units.
It implies, shaded area is;
Area trapezoid with parallel lengths 0.79505493571 units and 1 unit respectively, and height 1 unit - Area triangle with height 0.5 units and base 1 unit.
= (½(0.79505493571+1)*1)-(½*0.5*1)
= 0.89752746786-0.25
= 0.64752746786 square units.
