Mathematics Question and Solution

By Ogheneovo Daniel Ephivbotor
25th June, 2025

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.

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