Math Problem Statement

The lengths in meters of each of the boundary lines of a closed polygon are 411.5, 110.0, 279.1, 278.4, 334.0, 389.9, 40.3, 65.8, 40.7, 26.2, 52.3, 103.5, 36.0, 47.7, 111.1, 97.5, 105.3, 70.1, 23.3, 34.7, 63.8, 55.4, 90.0, 608.7, 395.1, 221.8, 152.3, 162.6, 301.1, 22.3, 107.2, 44.4, 130.0, 69.5, 38.6, 48.1, 52.0, 146.7, 114.3, 111.5, 47.7, 173.0, 87.9, 177.8, 152.1, 589.2. Calculate the total area of the closed polygon in square meters.

The lengths in meters of each of the boundary lines of a closed polygon are 411.5, 110.0, 279.1, 278.4, 334.0, 389.9, 40.3, 65.8, 40.7, 26.2, 52.3, 103.5, 36.0, 47.7, 111.1, 97.5, 105.3, 70.1, 23.3, 34.7, 63.8, 55.4, 90.0, 608.7, 395.1, 221.8, 152.3, 162.6, 301.1, 22.3, 107.2, 44.4, 130.0, 69.5, 38.6, 48.1, 52.0, 146.7, 114.3, 111.5, 47.7, 173.0, 87.9, 177.8, 152.1, 589.2. Calculate the total area of the closed polygon in square meters.

Solution

To calculate the area of the closed polygon, I will:

  1. Extract the coordinates or use the listed boundary lengths and determine if angles or bearings are given.
  2. Apply appropriate methods like the Surveyor's Formula (Shoelace Formula) or trapezoidal rule, depending on the data provided.

However, the image provided shows line lengths without additional data about angles or coordinates. For accurate calculation:

  • Are there coordinates, angles, or any additional data provided for these lengths?
  • If the data is based on bearings, I can calculate with further clarification.

Let me know, and I'll proceed!

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Math Problem Analysis

Mathematical Concepts

Geometry
Polygon Area Calculation
Surveyor's Formula (Shoelace Formula)

Formulas

Shoelace Formula: Area = 0.5 * |Σ(xi * yi+1 - yi * xi+1)|

Theorems

Surveyor's Theorem

Suitable Grade Level

Grades 10-12