How many square units are in its area?

Question

A quadrilateral has the the following vertices: (2,0),(4,5),(5,2),(1,4). How many square units are in its area? 

Answer 1

Plot the points on a coordinate system.  Then connect them so that they form a closed shape.  You now have your quadrilateral.  Next, you will use the distance formula 4 times to find the side lengths of the quadrilateral.

 

This distance formula is

 

d = √[(x₁ - x₂)² + (y₁ - y₂)²]

 

 

If your quadrilateral is NOT a parallelogram nor a rectangle, then you must have a trapezoid.  From this point on, you will divide the quadrilateral into two triangles.  You find the area of the 2 triangles and add them together.

 

 

Otherwise, multiply the length by the width to get the area.

Answer 2

Plotting the points is extremely important !  This may give you an idea for a strategy to find the area.

 

Leftmost point:      (1,4)

Rightmost point:    (5,2)

Lowest point:        (2,0)

Highest point:       (4,5)

 

Draw horizontal and vertical lines through those four points.  So, looking at the rectangle that encloses this figure, it is 4*5=20 square units.

 

But, there are 4 triangles that should not be counted.  Their areas are:

    (1/2)*1*4 = 2

    (1/2)*3*2 = 3

    (1/2)*1*3 = 3/2

    (1/2)*1*3 = 3/2

 

The area of the quadrilateral is 20 - 2 - 3 - 3/2 - 3/2 = 12 square units