Mathematics Question and Solution
Calculating Shaded Area.
a = 4(4)
a = 16 units.
a is AB.
b = a+4
b = 20 units.
b is AC.
It implies;
15²+20² = 7²+c²
225+400-49 = c²
c = 24 units.
c is CE.
d = ½(c)
d = 12 units.
d is CD = DE.
d' = atan(7/12)
d' = 30.2564371635°
d' is angle EDF.
e² = 12²+7²
e² = 144+49
e = √(193) units.
e = 13.8924439894 units.
e is DF.
f = atan(15/20)+ atan(7/24)
f = 53.1301023542°
f is angle ACE.
g² = 4²+12²-2*4*12cos53.1301023542
g = 10.1192885125 units.
g is BD.
(10.1192885125/sin53.1301023542) = (4/sinh)
h = asin(0.31622776602)
h = 18.4349488231°
j = 180-d'-h
j = 180-30.2564371635-18.4349488231
j = 131.308614013°
j is angle BFD.
Therefore, the required area, triangle BDF is;
0.5*DF*BDcosj
= 0.5*√(193)*10.1192885125sin131.308614013
= 52.8 square units.
