Penerapan Aturan Trapesium Dalam Integrasi Numerik Untuk Estimasi Luas Kota Mataram

Abstract

Accurate area estimation plays an essential role in spatial analysis, urban planning, and environmental monitoring. A common challenge arises from the limited accuracy of conventional methods in measuring regions with irregular geometries. This study aims to estimate the area of Mataram City by applying the Trapezoidal Rule, a numerical integration method implemented on boundary coordinate data digitized from Google Earth imagery. The analysis was conducted using three variations of partition numbers, namely 7, 14, and 28 segments, where each coordinate pair (x, y) represents the horizontal distance and vertical height of the partition. The results show that the 14-partition estimation yielded an area of 44.758 km² with the smallest relative error of 26.98% compared to the official area of Mataram City of 61.30 km². In contrast, the use of 7 and 28 partitions produced larger deviations. These findings indicate that selecting the appropriate number of partitions is crucial in improving estimation accuracy. Future research is recommended to examine other numerical methods such as Simpson’s rule or Gaussian quadrature, as well as to expand the study to different geographical regions in order to obtain more comprehensive results.