+0

# 03NS11

+1
184
5 Can anyone help please

Apr 8, 2019

#1
+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 :    Apr 8, 2019
#2
+2

Is there a way to do it with Shoelace Theorem?

ROYGBIV  Apr 8, 2019
#3
+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..   Apr 8, 2019
#4
+2

(-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
+2

Thank you!

ROYGBIV  Apr 9, 2019