We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
529
1
avatar+110 

Find the area of the quadrilateral formed with vertices at point (1,2) (5,8) (8,6) (4,0)

 Feb 7, 2018
 #1
avatar+102417 
+1

We can do this with something known as "Pick's Theorem"

 

Here's a pic  :

 

 

Area  =

 

Number of Interior Lattice Points  + Number of Border Lattice Points / 2   - 1

 

Where a "lattice point"  is a point with integer coordinates  [ in our case....the intersection of two gridlines]

 

Number of interior Lattice Points  = 24

 

Number of Border Lattice Points  =  6

 

So....the area is

 

24  +  6/2  + 1   =

 

24 + 3  - 1  =

 

26 units^2

 

 

cool cool cool

 Feb 8, 2018

9 Online Users

avatar