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5
avatar+44 

Can anyone help please

 Apr 8, 2019
 #1
avatar+99580 
+2

We can use something known as "Pick's Theorem" here

 

The area is given by :

 

Number of boundary lattice points on the triangle/ 2   + number of interior lattice points   -  1

 

Where a lattice point is one with integer coordinates 

 

Number of boundary lattice points  =  5  

 

Number of interior lattice points = 24

 

So

 

Total area  =    5/2 + 24 - 1  =   5/2 + 23  =   2.5 + 23  =

 

25.5  units^2

 

Here's the pic :

 

 

cool cool cool

 Apr 8, 2019
 #2
avatar+44 
+2

Is there a way to do it with Shoelace Theorem?

ROYGBIV  Apr 8, 2019
 #3
avatar+99580 
+1

I'm not familiar with this.....I checked my answer with WolframAlpha and it syncs up....

 

I see  that the Shoelace Theorem is on the internet....I'll look at it, and....if I can....I'll give you the solution using it..

 

 

cool cool cool

 Apr 8, 2019
 #4
avatar+99580 
+2

Here's your answer with the Shoelace Theorem

(-3, 2)       (6 , - 2)        (3, 5)

 (x1, y1)    (x2, y2)      (x3, y3)

 

The area is given by :

 

abs [ x1y2 + x2y3 + x3y1  - x1y3 - x2y1 - x3y2 ]

_________________________________________   =

                              2

 

abs [ (-3*-2) + (6*5) + (3*2) - (-3^5) - (6*2) - (3 * -2) ]

_____________________________________________   =

                             2

 

abs [ 6  + 30 + 6 - (-15)  - 12 - (-6) ]

_______________________________

                       2

 

abs [ 63 - 12 ] / 2  

 

51 / 2  =

 

25.5 units^2

 

Thanks for turning me on to this  !!!!.....I want to look at it a little more...I believe that it just involves a vector cross-product ......

 Apr 9, 2019
 #5
avatar+44 
+2

Thank you!

ROYGBIV  Apr 9, 2019

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