Given
AB=11yd
DA=8yd
Angle BCD = 72 degree
Angle CDA = 65 degree
Find
1. Area
2. Perimeter
Explanation
Construction - draw a perpendicular from B to F and A to E
In triangle ADE
[tex]\begin{gathered} sin65=\frac{AE}{8} \\ AE=8\times sin65 \\ AE=7.25 \end{gathered}[/tex]
Now using the Pythogoras theorem to find x
[tex]\begin{gathered} 8^2=x^2+7.25^2 \\ x^2=64-52.5625 \\ x=3.38 \end{gathered}[/tex]
Since AE=BF
So BF = 7.25
[tex]\begin{gathered} sin72=\frac{7.25}{BC} \\ BC=7.623 \end{gathered}[/tex]
Using Pythogoras theorem to find y
[tex]\begin{gathered} 7.623^2=7.25^2+y^2 \\ y=\sqrt{58.110129-52.5625} \\ y=2.35534\text{ yd} \end{gathered}[/tex]
Perimeter = AB+BC+CD+DA
11 + 7.623 + 11 + 3.38 + 2.35534 + 8 = 51.35834 yd
Area=
[tex]\begin{gathered} A=\frac{1}{2}(sum\text{ }of\text{ }parrallel\text{ }sides)\times height \\ =\frac{1}{2}(11+2.35534+3.38)\times7.25 \\ =60.6656\text{ }yd^2 \end{gathered}[/tex]
Final Answer
Perimeter = 51.35834 yd
Area = 60.6656 yd square
