Question

Find the area and perimeter of the trapezoid. See picture for full problem. Please and thank you so very much!

Answer 1

The area of the trapezoid is 22.5 square miles.

The perimeter of the trapezoid is 22.5 miles.

Explanation:

Recall that the area of a trapezoid is given by:

`\displaystyle A = (1)/(2)(b_1+b_2)h`

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:

`\displaystyle \begin{aligned} A & = (1)/(2)(5.5+3.5)(5) \\ \\ & = (1)/(2)(9)(5) \\ \\ & = (45)/(2) \\ \\ &= 22.5\text{ mi}^2\end{aligned}`

The perimeter of the trapezoid is simply the sum its four sides. Hence:

`\displaystyle \begin{aligned} P & = (5.5) + (6) + (7.5) + (3.5) \\ \\ & = 22.5\text{ mi} \end{aligned}`

Therefore, the area and perimeter of the trapezoid is 22.5 square miles and 22.5 miles, respectively.