Mathematics Question and Solution
(2√(2)/sin135) = (√(2)/sina)
a = 20.70481105464°
b = 180-20.70481105464-135
b = 24.29518894536°
(c/sin24.29518894536) = (2√(2)/sin135)
c = 1.64575131106 units.
Where c is the height of the yellow inscribed trapezoid.
(2√(2)/sin45) = (√(2)/sind)
d = 20.70481105464°
e = 180-20.70481105464-45
e = 114.29518894536°
(2√(2)/sin45) = (f/sin114.29518894536)
f = 3.64575131106 units.
Where f is the base parallel length of the inscribed yellow trapezoid.
g = 90-20.70481105464
g = 69.29518894536°
h = 180-2(69.29518894536)
h = 41.40962210928°
(i/sin41.40962210928) = (2√(2)/sin69.29518894536)
i = 2 units.
Where i is the top parallel length of the inscribed yellow trapezoid.
Therefore;
Area inscribed yellow trapezoid is;
½(i+f)*c
= 0.5(2+3.64575131106)*1.64575131106
= 4.64575131105 square units.
