<p> data isolated </p>

ab6afc29-861c-4d3c-b86a-60e9d566281e 8 15 12 decimal

&[DATE] &[TIME] - &[FILENAME]

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

1. Regular Polygon Area/Perimeter

N 5 :

n 13 :

m 4 :

'a' vertices a N 1 - :

'b' vertices b n 1 - :

'c' vertices c m 1 - :

j 1 N range sqr j 1 el j a / 2 * π * cos : sqr j 2 el j a / 2 * π * sin : 21 line for sqr 21 line

j 1 n range circle j 1 el j b / 2 * π * cos : circle j 2 el j b / 2 * π * sin : 21 line for circle 21 line

j 1 m range tria j 1 el j c / 2 * π * cos : tria j 2 el j c / 2 * π * sin : 21 line for tria 21 line

θ rot θ cos θ sin - θ sin θ cos 22 mat :

data tria :

θ π 2 / :

θ 1.5708

vertices 2 circle * . 10 black plot :

NOT commutative Triangle tria θ rot * :

sqr circle 2 * Triangle 2 * vertices 4 1 sys

x data 1 col : y data 2 col : 12 mat Area 12 / x i el y i 1 + el * x i 1 + el y i el * - (i 1 x rows 1 - sum * : Perimeter x i 1 + el x i el - (2^y i 1 + el y i el - (2^+ sqrt i 1 x rows 1 - sum : 31 sys

native figure ...
i.e: NOT as plotted Area Perimeter 21 mat 1.299 5.196 21 mat

2. Irregular Polygon Area/Perimeter

data spec pts i 1 data rows range p i el a b c spec : for v p 1 el : Unest 'p' j 2 p rows range v v p j el stack : for data v augment 51 line :

A method for finding the area of any polygon when the coordinates of its vertices are known

x 24911215 mat transpose :

y 2972215 mat transpose :

uv x y augment :

Area Polygon wrt vertices coordinates A 12 / x i el y i 1 + el * x i 1 + el y i el * - (i 1 x rows 1 - sum * abs :

a b c spec . 14 red 13 mat : XY uv a b c spec pts : 21 sys

Perimeter is calculated wrt each hypotenuse from the projections ... Inspect the plot.

uv XY 4 2 + 20 black 1 5 mat 9 2 + 20 black 1 5 mat 4 7 + 20 black 1 5 mat 5 1 sys

uv 2249971122252 mat

Perimeter  Polygon wrt vertices coordinates P x i 1 + el x i el - (2^y i 1 + el y i el - (2^+ sqrt i 1 x rows 1 - sum :

A P 12 mat 42 27.05 12 mat

A P 21 mat 42 27.05 21 mat

3. Odd shape Area/Perimeter

<p> data isolated </p>

data 410419728133717462055196417731582159122992810236103441045210360102681017610084999298100981089811698124981329814097148951569116382167701695617143173341732717223163141541114511136121271411817109201002491288226732064145510467374282192104532 mat :

x data 1 col : y data 2 col : 12 mat pts data o 5 red plot : 21 sys

data rows 53

Area Polygon wrt vertices coordinates A 12 / x i el y i 1 + el * x i 1 + el y i el * - (i 1 x rows 1 - sum * abs :

Perimeter  Polygon wrt vertices coordinates P x i 1 + el x i el - (2^y i 1 + el y i el - (2^+ sqrt i 1 x rows 1 - sum :

sub data 125 range 12 range el : x sub 1 col : y sub 2 col : 12 mat arc x i 1 + el x i el - (2^y i 1 + el y i el - (2^+ sqrt i 1 x rows 1 - sum : Arc sub . 14 black plot : 41 sys

data pts Arc 3 1 sys

Area native data
Perim native data
Arc length sub A P arc 31 mat 1314847920731 mat