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A quadrilateral has four points A(0,1), B(1,3), C(5,2) and D(4,1) as coordinates, how do I find the area?

 Jul 10, 2021
 #1
avatar+126 
+4

Answer: \(6.5\) \(units²\)

 

Solution:

I would think that the best way is to graph the shape (although there is probably some better way) and then to break it up into three triangles and a rectangle. You can find the area of a triangle by looking at the graph, or just by looking at its points. (1-0)(3-1)/2 = 1 for example on the first triangle. I'm not great at explaining, so sorry if this doesn't make sense.

 

Triangle 1: (0,1), (1,1), (1,3)

The area of Triangle 1 is 1 square unit.

Triangle 2: (1,3), (1,2), (5,2)

The area of Triangle 2 is 2 square units.

Triangle 3: (5,2), (4,2), (4,1)

The area of Triangle 3 is 0.5 square units.

Rectangle: (1,1), (1,2), (4,2), (4,1)

The area of the rectangle is 3 square units.


Adding them all up you get 1 + 2 + 0.5 + 3 = \(6.5\) \(units²\)

 Jul 10, 2021
 #2
avatar+114788 
+1

I graphed it

then I added X(1,1)  and E(5,1)

 

Area = area of triangle ABX +  Area of trapezium XBCE  -  area of triangle DCE

 

Area = 1+ (3/2 * 4) - 0.5

Area = 1 + 6 - 0.5

Ara = 6.5 unites square

 Jul 10, 2021

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