MATH SOLVE

3 months ago

Q:
# Estimate the area of Alberta in square miles. Show your reasoning

Accepted Solution

A:

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].