Measuring areas on maps: The area of an irregular figure on a plotted map or plan is commonly measured with which instrument?

Introduction / Context:
Estimating land areas from maps is a frequent task in civil engineering and surveying. Irregular boundaries make arithmetic methods cumbersome; hence, mechanical integrators like the planimeter provide a quick and accurate solution by tracing the boundary directly on the plan.

Given Data / Assumptions:

• A scaled plan or map is available.
• The boundary to be measured may be curved or irregular.
• Instrument constants have been checked or calibrated.

Concept / Approach:
A planimeter converts the path traced by its measuring wheel into an area reading. The final reading, multiplied by the square of the map scale, yields ground area. Other listed instruments serve different purposes: pantographs scale drawings, sextants measure celestial/sea angles, clinometers measure vertical angles, and optical squares set right angles in chain surveying.

Step-by-Step Solution:

Verification / Alternative check:
Compare with a grid-square counting method on a transparent overlay; results should agree within acceptable tolerance.

Why Other Options Are Wrong:

• Pantograph, sextant, clinometer, and optical square do not measure areas directly.

Common Pitfalls:
Tracing too fast causing wheel slip; not closing the figure precisely; forgetting to apply the plan scale correctly, leading to large percentage errors.

Final Answer:
Planimeter (for direct area measurement)