Question

a map of utah is shown. which area is closest to the area of utah?
165 miles
70
miles
105 miles
350
miles
280
miles
270 miles
a. 1,240 square miles
b. 87,150 square miles
c. 94,500 square miles
d. 119,000 square mile
problem 6
he is a picture of a circle. each square represents 1 square unit.

Explanation:

Step1: Divide the map into shapes

Divide the map of Utah into a rectangle and a trapezoid.

Step2: Calculate the area of the rectangle

The rectangle has length \(350\) miles and width \(270\) miles.
The area of a rectangle \(A_{1}=l\times w = 350\times270=94500\) square miles.

Step3: Calculate the area of the trapezoid

The trapezoid has bases \(b_{1}=165\) miles and \(b_{2}=270\) miles, and height \(h = 70\) miles.
The area of a trapezoid \(A_{2}=\frac{(b_{1} + b_{2})h}{2}=\frac{(165 + 270)\times70}{2}=\frac{435\times70}{2}=15225\) square miles.

Step4: Calculate the total area

The total area \(A=A_{1}+A_{2}=94500 + 15225=109725\) square miles.

Answer:

The area closest to \(109725\) square miles is \(119000\) square miles (Option D).