Given:-
A tapezoid.
To find the area.
To find the distance we use the formula,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
So now we find the distance of AD is,
[tex]\begin{gathered} d=\sqrt{(0-16)^2+(13-1)^2} \\ d=\sqrt{16^2+12^2} \\ d=\sqrt{256+144} \\ d=\sqrt{400} \\ d=20 \end{gathered}[/tex]
So the distance of AD is 20.
So now we find the distance of BC,
[tex]\begin{gathered} d=\sqrt{(5-1)^2+(3-6)^2} \\ d=\sqrt{4^2+(-3)^2} \\ d=\sqrt{16^+9} \\ d=\sqrt{25} \\ d=5 \end{gathered}[/tex]
So the distance of BC is 5.
So now the area of trapezoid is,
[tex]\begin{gathered} A=\frac{a+b}{2}(h) \\ A=\frac{20+5}{2}(5) \\ A=\frac{25}{2}(5) \\ A=\frac{125}{2} \\ A=62.5 \end{gathered}[/tex]
So the required area is 62.5 sq units.
