Question

type the correct answer in the box. use numerals instead of words.
the shape of a township with a population of 12,620 people is shown.
image of an l - shaped figure with dimensions 40 mi, 25 mi, 25 mi, 60 mi
what is the population density to the nearest tenth?
the population density is approximately
people per square mile.

Explanation:

Step1: Calculate the area of the township

We can divide the shape into two rectangles.
First rectangle: length = 60 mi, width = 25 mi. Area of first rectangle: $A_1 = 60\times25 = 1500$ square miles.
Second rectangle: length = 40 mi, width = (60 - 25) = 35 mi? Wait, no, looking at the diagram, the vertical side is 40 mi and 25 mi, horizontal side is 60 mi. Wait, maybe better to split as: one rectangle with length 60 mi and height (25 + 40) = 65 mi, but then subtract the missing part. Wait, no, the shape is like a large rectangle minus a smaller rectangle? Wait, no, the diagram: the bottom part is 25 mi height, 60 mi length. The top part is 40 mi height, and the horizontal length is (60 - 25) = 35 mi? Wait, maybe I misread. Wait, the given dimensions: 25 mi (vertical), 25 mi (horizontal), 40 mi (vertical), 60 mi (horizontal). Let's split the shape into two rectangles:

1. Bottom rectangle: length = 60 mi, height = 25 mi. Area: $60\times25 = 1500$ sq mi.
2. Top rectangle: length = (60 - 25) = 35 mi? Wait, no, the vertical side is 40 mi, and the horizontal side: the total horizontal length is 60 mi, and the bottom rectangle has 25 mi horizontal? Wait, maybe the correct split is: the shape is a rectangle of 60 mi (length) and (25 + 40) = 65 mi (height), minus a rectangle of 25 mi (length) and 40 mi (height)? Wait, no, let's look at the diagram again. The figure has a notch: the bottom part is 25 mi tall, 60 mi long. The top part is 40 mi tall, and the horizontal length is (60 - 25) = 35 mi? Wait, maybe the correct way is:

First rectangle: width = 25 mi, height = 60 mi. Area: $25\times60 = 1500$ sq mi.

Second rectangle: width = 40 mi, height = (60 - 25) = 35 mi? No, that doesn't make sense. Wait, maybe the vertical sides: 25 mi and 40 mi, so total height is 25 + 40 = 65 mi. The horizontal side: 60 mi, but there's a 25 mi indentation. So the area is (65\times60) - (25\times40)? Wait, no, that would be if the notch is 25 mi wide and 40 mi tall. Wait, let's calculate the area correctly.

Alternative approach: The shape can be divided into two rectangles:

- Rectangle 1: length = 60 mi, height = 25 mi. Area: $60\times25 = 1500$ sq mi.
- Rectangle 2: length = (60 - 25) = 35 mi? No, wait, the vertical side is 40 mi, and the horizontal side: the top rectangle has length (60 - 25) = 35 mi? No, maybe the top rectangle is 40 mi tall and (60 - 25) = 35 mi long? Wait, no, the given 25 mi (horizontal) and 25 mi (vertical), 40 mi (vertical), 60 mi (horizontal). Let's do:

Total area = (60 * 25) + ( (60 - 25) * 40 )

Calculate (60 - 25) = 35. Then (35 * 40) = 1400. Then total area = 1500 + 1400 = 2900? Wait, no, that can't be. Wait, maybe I made a mistake. Wait, 60 - 25 is 35, 35 * 40 is 1400, 60 *25 is 1500, sum is 2900. Wait, but let's check again. The bottom rectangle is 60 mi long, 25 mi tall: area 1500. The top rectangle is (60 - 25) = 35 mi long, 40 mi tall: area 35*40=1400. Total area 1500+1400=2900 square miles.

Step2: Calculate population density

Population density = Population / Area. Population is 12620 people. Area is 2900 sq mi. So density = 12620 / 2900 ≈ 4.3517... Rounding to the nearest tenth: 4.4? Wait, wait, did I calculate the area correctly? Wait, maybe the area is different. Wait, let's re-examine the diagram. Maybe the correct split is:

The shape is a rectangle with length 60 mi and height (25 + 40) = 65 mi, minus a rectangle with length 25 mi and height 40 mi. So area = (60*65) - (25*40) = 3900 - 1000 = 2900. Yes, that's the same as before. So area is 2900 sq mi.

Then population density = 12620 / 2900 ≈ 4.3517, which to the nearest tenth is 4.4? Wait, 12620 divided by 2900: 2900*4 = 11600, 12620-11600=1020, 1020/2900≈0.3517, so total≈4.3517, which is 4.4 when rounded to the nearest tenth. Wait, but maybe I made a mistake in the area. Wait, let's check again.

Wait, another way: the figure has two rectangles. First: 25 mi (height) x 60 mi (length) = 1500. Second: 40 mi (height) x (60 - 25) mi (length) = 40 x 35 = 1400. 1500 + 1400 = 2900. Correct. Then 12620 / 2900 = let's compute that. 2900 * 4 = 11600, 12620 - 11600 = 1020. 1020 / 2900 ≈ 0.3517. So total is 4.3517, which is 4.4 when rounded to the nearest tenth.

Wait, but maybe the area is different. Wait, maybe the vertical sides: 25 mi and 40 mi, so total height is 25 + 40 = 65 mi. The horizontal side: 60 mi, but there's a 25 mi indentation. So the area is 60*65 - 25*40 = 3900 - 1000 = 2900. Correct. So population density is 12620 / 2900 ≈ 4.4 (to the nearest tenth).

Answer:

4.4