Concept:
A planimeter is a surveying instrument used to determine the area of irregular figures drawn on maps, plans, and contour maps.
Step 1: Recall the functions of the instruments.
• Planimeter $\rightarrow$ Measures area.
• Clinometer $\rightarrow$ Measures slope or vertical angle.
• Graphometer $\rightarrow$ Measures horizontal angles.
• Areameter is not the standard surveying instrument used for contour maps.
Step 2: Identify the correct instrument.
Hence,
\[
\boxed{\text{Planimeter is used to measure areas on maps}.}
\]
Therefore, the correct option is
\[
\boxed{(C)\;\text{Planimeter}.}
\]