we have three figures, we must find the area of each one and at the end, add them
lower triangle
we must find x and y to calculate the area, we will use trigonometric ratios
[tex]\begin{gathered} \sin (80)=\frac{x}{200} \\ \\ x=200\sin (80) \\ x=197 \end{gathered}[/tex][tex]\begin{gathered} \sin (10)=\frac{y}{200} \\ \\ y=200\sin (10) \\ y=34.73 \end{gathered}[/tex]
now calculate the area
[tex]\begin{gathered} A_{T1}=\frac{b\times h}{2} \\ \\ A_{T1}=\frac{y\times x}{2}=\frac{34.73\times197}{2} \\ \\ A_{T1}_{}=3420.9 \end{gathered}[/tex]
the area of the triangle is 3420.9 square feet
Rectangle
we have the height (160ft) and the base we calculate it in the previous step (x=197ft)
the area is
[tex]\begin{gathered} A_R=b\times h \\ A_R=197\times160 \\ A_R=31520 \end{gathered}[/tex]
the area of the rectangle is 31520 square feet
Left Triangle
we must use trigonometric ratios to calculate Z
[tex]\begin{gathered} \tan (15)=\frac{Z}{160+34.73} \\ \\ Z=194.73\tan (15) \\ Z=52.18 \end{gathered}[/tex]
and the area of the triangle is
[tex]\begin{gathered} A_{T2}=\frac{b\times h}{2} \\ \\ A_{T2}=\frac{Z\times(160+34.73)}{2}=\frac{52.18\times194.73}{2} \\ \\ A_{T2}=5080.5 \end{gathered}[/tex]
Total area
[tex]\begin{gathered} A=A_{T1}+A_R+A_{T2} \\ A=3420.9+31520+5080.5 \\ A=40021.4 \end{gathered}[/tex]
the total area is 40,021.4 square feet
