A land plot is defined by points A(0,0), B(4,0), C(5,3), D(1,3). What is the area of the parallelogram representing this plot?
12
Given: the parallelogram has vertices A(0,0), B(4,0), C(5,3) and D(1,3).
Area of a parallelogram = base × perpendicular height.
Take AB as the base. Since A(0,0) and B(4,0) both lie on the x-axis, the base length \(AB = 4\) units.
The opposite side DC lies along the line \(y = 3\) (points D(1,3), C(5,3)), so the perpendicular distance between AB and DC is the height.
Height \(h = 3 - 0 = 3\) units.
Area \(= \text{base} \times \text{height} = 4 \times 3 = 12\) square units.
Hence the area of the parallelogram plot is 12 square units.
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