Solutions to the Above Problems

1. Solution
   
   We first determne the dimensions needed to calculate the area then use the formulas for each figure.
   
   

   1. The figure in part a) is a rectangle of width AD = 3 units and length DC = 4 units. Hence the area is given by
      Area = Length × witdh = 4 × 3 = 12 unit ²

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   2. The figure in part b) is a square of side HG = 3 units. Hence the area is given by
      Area = Side × Side = 3 × 3 = 9 unit ²

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   3. The figure in part c) is a right triangle of height H = ML = 3 and base B = MN = 4. The area is given by
      Area = (1 / 2) × H × B = (1 / 2) × 3 × 4 = 6 unit ²

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   4. The figure in part d) is a right triangle of same dimension as the right triangle in part c): Height H = IJ = 3 and base B = JK = 4. The area is given by
      Area = (1 / 2) × H × B = (1 / 2) × 3 × 4 = 6 unit ²

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   5. The figure in part e) is a parallelogram of length L = OP = 5 units and the distance H between OP and RQ = 3 units (see figure below) . The area is given by
      

      .

      
      Area = L × H = 5 × 3 = 15 unit ²
      Note that H is perpendicular to both OP and RQ.

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2. Solution
   
   We first need to identify the figure, determine its dimensions and then calcualte the area.
   
   

   1. The figure in part a) is a trapezoid with AB and DC parallel. Base B₁ = DC = 2 units, base B₂ = AB = 4 and the height H = AD = 3 units. Hence the area is given by
      Area = (1 / 2) × H × (B₁ + B₂) = ( 1 / 2) × 3 × (2 + 4) = ( 1 / 2) × 3 × 6 = (1 / 2) × 18 = 18 / 2 = 9 unit ²

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   2. The figure in part b) is a trapezoid with GF and HE parallel. Base B₁ = GF = 2 units, base B₂ = HE = 4 and the height H = 2 units. Hence the area is given by
      Area = (1 / 2) × H × (B₁ + B₂) = ( 1 / 2) × 2 × (2 + 4) = ( 1 / 2) × 2 × 6 = (1 / 2) × 12 = 12 / 2 = 6 unit ²

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   3. The figure in part c) is a triangle of base B = LN = 5 units and height H = 4 units (see figure below). The area is given by
      

      .

      
      Area = (1 / 2) × B × H = (1 / 2) × 5 × 4 = (1 / 2) × 20 = 20 / 2 = 10 unit ²

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   4. The figure in part d) is a triangle of base B = IK = 4 units and height H = 4 units (see figure below). The area is given by
      
      

      .

      
      
      Area = (1 / 2) × B × H = (1 / 2) × 4 × 4 = (1 / 2) × 16 = 16 / 2 = 8 unit ²

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   5. The figure in part e) is a trapezoid with base B₁ = OP = 2 units, base B₂ = RQ = 7 units and height H = 3. . The area is given by
      
      Area = (1 / 2) × H × (B₁ + B₂) = ( 1 / 2) × 3 × (2 + 7) = ( 1 / 2) × 2 × 9 = (1 / 2) × 27 = 27 / 2 = 13.5 unit ²

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