Mathematics Question and Solution
a = ⅓(4L)-L
a = ⅓(L) cm.
tanb = L/(4L/3)
b = atan(3/4)°
3/4 = c/(⅓(L))
c = ¼(L) cm.
d = 180-45-atan(3/4)
d = (45+atan(4/3))°
It implies;
((4L/3)/sin(45+atan(4/3))) = (e/sin(atan(3/4)))
e = 0.8081220356L cm.
Calculating L.
(0.5*0.8081220356L*(4L/3)sin45)-(0.5*(L/3)*(L/4) = 342/7
0.380952381L²-0.0416666667L² = 342/7
2.375L² = 342
L = 12 cm.
Recall.
e = 0.8081220356L
And L = 12 cm.
e = 0.8081220356*12
e = 9.6974644272cm.
Therefore, red area exactly in decimal is;
(½*12*12)-(0.5*9.6974644272*12sin45)
= 72-41.1428571407
= 30.8571428593 cm²
