Question:
Draw a quadrilateral in Cartesian plane, whose vertices are ( 4,5), (0,7), (5, 5) and ( 4, 2). Also find its area
Answer:
Let ABCD is the given quadrilateral with vertices A(-4, 5), B(0, 7), C(5, -5) and D(-4, -2)
The quadrilateral ABCD is drawn which is shown in the figure.
Now, Area(ABCD) = Area(Δ ABC) + Area(Δ ACD)
Area(Δ ABC) = (1/2)*|-4(7+5) + 0(-5+5) + 5(5-7)|
= (1/2)*|-4*12 + 5(-2)|
= (1/2)*|-48 - 10|
= (1/2)*|-58|
= 58/2
= 29
Area(Δ ACD) = (1/2)*|-4(5+2) + 5(-2-5) + (-4)*(5+5)|
= (1/2)*|-4*(-3) + 5(-7) - 4*10|
= (1/2)*|12 - 35 - 40|
= (1/2)*|-63|
= 63/2
= 28
Now, Area(ABCD) = Area(Δ ABC) + Area(Δ ACD)
= 29 + 63/2
= (58 + 63)/2
= 121/2 square unit
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