Area by Trapezoidal Rule

The trapezoidal rule estimates an irregular area by replacing each curved or sloping section of the boundary with a trapezium. Each pair of neighbouring offsets gives a strip whose area is the strip width multiplied by the average of its two end heights, and adding all the strips gives the total area. The end ordinates are counted once, while the interior ordinates are shared between two adjacent strips, which is why the formula has half-weight at the ends and full-weight in the middle.

Use this in surveying when you know a series of offsets from a baseline to an irregular boundary and need the enclosed area quickly. It is common for land parcels, river cross-sections, roadworks, and earthworks when the boundary is too irregular for a simple geometric shape.

• Forgetting that the first and last offsets are halved, not added in full
• Using the wrong strip width when the offsets are not equally spaced
• Mixing up metres and square metres, especially when reporting the final area