Assume an idealized square township exactly 6 miles on each side. What is its area in square miles?
Correct Answer
D) 36 square miles
Idealized area=6 miles×6 miles=36 square miles. Common errors: computing the perimeter instead of the area gives 24 square miles; adding the sides instead of multiplying them gives 12 square miles; reporting one side length gives 6 square miles.
Why This Is the Correct Answer
Option D is correct because idealized area = 6 miles x 6 miles = 36 square miles. This matches the rectangular survey system, in which each township is divided into 36 sections of approximately one square mile each.
Why the Other Options Are Wrong
Option A: 6 square miles
Option A is wrong because 6 square miles simply reports one side length. Area requires multiplying the sides: 6 x 6 = 36 square miles.
Option B: 12 square miles
Option B is wrong because 12 square miles comes from adding the sides (6 + 6) instead of multiplying them. The correct calculation is 6 x 6 = 36 square miles.
Option C: 24 square miles
Option C is wrong because 24 square miles comes from computing the perimeter (6 x 4) instead of the area. Area is 6 x 6 = 36 square miles.
Six by six is 36
A township is 6 miles by 6 miles, which gives 36 square miles and 36 sections.
How to use: Use this match between area and section count to check township answers.
Exam Tip
For area, multiply length by width; if the answer equals the perimeter or a single side, you used the wrong operation.
Common Mistakes to Avoid
- -Computing perimeter instead of area
- -Adding sides instead of multiplying
- -Confusing a township with a single section
Concept Deep Dive
Analysis
This question tests a simple area calculation for an idealized township. Area of a square is side times side, so 6 miles x 6 miles = 36 square miles. The distractors come from computing perimeter, adding sides or reporting one side.
Background Knowledge
In the rectangular (government) survey system, a township is nominally 6 miles square. Each township is divided into 36 sections of approximately one square mile, or 640 acres. Actual townships can vary because of survey corrections and the curvature of the earth.
Real-World Application
An appraiser reading a rural legal description notes the property lies in a numbered section within a township. Knowing a township holds 36 sections of about one square mile helps the appraiser locate the parcel on survey maps.
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