Answer: About [tex]278,250\ mi^2[/tex]
Step-by-step explanation:
The missing figure is attached.
Notice in the first picture that Alberta has a complex shape.
You can calculate the area of a complex shape by decomposing it into polygons whose areas can be calculated easily.
Observe the second picture. Notice that it can be descompose into two polygons: A trapezoid and a rectangle.
The area of the trapezoid can be calcualted with the formula:
[tex]A_t=\frac{h}{2}(B+b)[/tex]
Where "h" is the height, "B" is the long base and "b" is short base.
And the area of the rectangle can be found with the formula:
[tex]A_r=lw[/tex]
Wkere "l" is the lenght and "w" is the width.
Then, the apprximate area of Alberta is:
[tex]A=\frac{h}{2}(B+b)+lw[/tex]
Substituting vallues, you get:
[tex]A=(\frac{(410\ mi-180\ mi)}{2})(760\ mi+470\ mi)+(180\ mi)(760\ im)\\\\A=141,450\ mi^2+136,800\ mi^2\\\\A=278,250\ mi^2[/tex]
Therefore, the area of of Alberta is about [tex]278,250\ mi^2[/tex].
