This geography problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.
ScanSolve AI Answer
Hey Dr., good to see you again. a) Two units used for area measurement are: • Square meters (m^2) • Hectares (ha) b) Two types of surface areas in the context of land surveying are: • Horizontal surface area: This is the area projected onto a horizontal plane, which is typically what is calculated for land plots using coordinates. • Sloping surface area: This is the actual physical surface area of the land, taking into account its undulations and slopes. It is always greater than or equal to the horizontal surface area. c) Calculate the surface area of the land. The coordinates are given as (East, North). We will use the shoelace formula for the area of a polygon. Points: A: (x_1, y_1) = (364.392, 674.345) B: (x_2, y_2) = (526.937, 715.825) C: (x_3, y_3) = (682.910, 562.826) D: (x_4, y_4) = (561.039, 328.426) E: (x_5, y_5) = (385.491, 351.813) Step 1: Calculate the sum of products x_i y_i+1 (with y_n+1 = y_1). S_1 = x_1y_2 + x_2y_3 + x_3y_4 + x_4y_5 + x_5y_1 S_1 = (364.392 × 715.825) + (526.937 × 562.826) + (682.910 × 328.426) + (561.039 × 351.813) + (385.491 × 674.345) S_1 = 260773.8064 + 296568.0496 + 224213.9166 + 197305.5785 + 259850.5960 S_1 = 1238711.9471 Step 2: Calculate the sum of products y_i x_i+1 (with x_n+1 = x_1). S_2 = y_1x_2 + y_2x_3 + y_3x_4 + y_4x_5 + y_5x_1 S_2 = (674.345 × 526.937) + (715.825 × 682.910) + (562.826 × 561.039) + (328.426 × 385.491) + (351.813 × 364.392) S_2 = 355397.0267 + 489006.1825 + 315790.6620 + 126622.7507 + 128290.4709 S_2 = 1415107.0928 Step 3: Calculate the area using the shoelace formula. Area = (1)/(2) |S_1 - S_2| Area = (1)/(2) |1238711.9471 - 1415107.0928| Area = (1)/(2) |-176395.1457| Area = (1)/(2) × 176395.1457 Area = 88197.57285 Step 4: Round the area to two decimal places. The surface area of the land is 88197.57 square units. d) Calculate the perimeter of the portion. Figure 2, which is referenced in this part of the question, is not provided in the image. Therefore, it is not possible to calculate the perimeter of the portion without the additional information from Figure 2. Send me the next one 📸