Answer:
The area of the trapezoid is 22.5 square miles.
The perimeter of the trapezoid is 22.5 miles.
Step-by-step explanation:
Recall that the area of a trapezoid is given by:
[tex]\displaystyle A = \frac{1}{2}(b_1+b_2)h[/tex]
Where b₁ and b₂ are the two parallel bases and h is the vertical height between them.
The two bases are 5.5 mi and 3.5 mi and the vertical height between them is 5 mi. Hence, the area of the trapezoid is:
[tex]\displaystyle \begin{aligned} A & = \frac{1}{2}(5.5+3.5)(5) \\ \\ & = \frac{1}{2}(9)(5) \\ \\ & = \frac{45}{2} \\ \\ &= 22.5\text{ mi}^2\end{aligned}[/tex]
The perimeter of the trapezoid is simply the sum its four sides. Hence:
[tex]\displaystyle \begin{aligned} P & = (5.5) + (6) + (7.5) + (3.5) \\ \\ & = 22.5\text{ mi} \end{aligned}[/tex]
Therefore, the area and perimeter of the trapezoid is 22.5 square miles and 22.5 miles, respectively.
