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A) What are two units used for area measurement? b) What are two types of surface areas in land surveying? c) Calculate the surface area of the land given the coordinates.

Geography

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Answer

c

88197.57 square units\text{88197.57 square units}

Step-by-step solution

4 steps

Part a

Two units used for area measurement are

  • Square meters (m2\text{m}^2)
  • Hectares (ha\text{ha})

Part 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.

Part c

88197.57 square units\text{88197.57 square units}

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: (x1,y1)=(364.392,674.345)(x_1, y_1) = (364.392, 674.345)
B: (x2,y2)=(526.937,715.825)(x_2, y_2) = (526.937, 715.825)
C: (x3,y3)=(682.910,562.826)(x_3, y_3) = (682.910, 562.826)
D: (x4,y4)=(561.039,328.426)(x_4, y_4) = (561.039, 328.426)
E: (x5,y5)=(385.491,351.813)(x_5, y_5) = (385.491, 351.813)

  1. Calculate the sum of products xiyi+1x_i y_{i+1} (with yn+1=y1y_{n+1} = y_1).

    S1=x1y2+x2y3+x3y4+x4y5+x5y1S_1 = x_1y_2 + x_2y_3 + x_3y_4 + x_4y_5 + x_5y_1 S1=(364.392×715.825)+(526.937×562.826)+(682.910×328.426)+(561.039×351.813)+(385.491×674.345)S_1 = (364.392 \times 715.825) + (526.937 \times 562.826) + (682.910 \times 328.426) + (561.039 \times 351.813) + (385.491 \times 674.345) S1=260773.8064+296568.0496+224213.9166+197305.5785+259850.5960S_1 = 260773.8064 + 296568.0496 + 224213.9166 + 197305.5785 + 259850.5960 S1=1238711.9471S_1 = 1238711.9471
  2. Calculate the sum of products yixi+1y_i x_{i+1} (with xn+1=x1x_{n+1} = x_1).

    S2=y1x2+y2x3+y3x4+y4x5+y5x1S_2 = y_1x_2 + y_2x_3 + y_3x_4 + y_4x_5 + y_5x_1 S2=(674.345×526.937)+(715.825×682.910)+(562.826×561.039)+(328.426×385.491)+(351.813×364.392)S_2 = (674.345 \times 526.937) + (715.825 \times 682.910) + (562.826 \times 561.039) + (328.426 \times 385.491) + (351.813 \times 364.392) S2=355397.0267+489006.1825+315790.6620+126622.7507+128290.4709S_2 = 355397.0267 + 489006.1825 + 315790.6620 + 126622.7507 + 128290.4709 S2=1415107.0928S_2 = 1415107.0928
  3. Calculate the area using the shoelace formula.

    Area=12∣S1−S2∣Area = \frac{1}{2} |S_1 - S_2| Area=12∣1238711.9471−1415107.0928∣Area = \frac{1}{2} |1238711.9471 - 1415107.0928| Area=12∣−176395.1457∣Area = \frac{1}{2} |-176395.1457| Area=12×176395.1457Area = \frac{1}{2} \times 176395.1457 Area=88197.57285Area = 88197.57285
  4. Round the area to two decimal places.

    The surface area of the land is 88197.57 square units\boxed{\text{88197.57 square units}}.

Part 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.

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