Mathematics Question and Solution

By Ogheneovo Daniel Ephivbotor
5th June, 2025

Notice.


Triangle ACD and Triangle BCD are right-angled triangles.


Let AD = 2 units.


AB = 6 units.


It implies;


BD = 6-2

BD = 4 units.


a² = 2(0.5*4)²

a = 2√(2) units.

a is BE = CE.


tanb = (2/4)

b = atan(½)°

b is angle DAF.


Therefore;


DF = 1 units.


Area triangle AFD is;

½(AD)*(DF)

= ½*2*1

= 1 square units.


Calculating area triangle CFE.


It implies;


Area trapezoid with parallel lengths 2 unit and 4 units respectively and height 2 units - Area trapezoid with parallel lengths 1 unit and 2 units respectively and height 2 units.


(½(4+2)*2)-(½(2+1)*2)

= 6-3

= 3 square units.


Area AFD ÷ Area CFE is;


= ⅓

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