"What is the area? You should be able to solve this"

[roadrunner]

On the hp prime I used the geometry app:

Code:

"GA:= point(0.,0.); // c(FF000000) v(1) 
GB:= point(xyc,0.); // c(FF000000) v(1) 
GC:= point(xyc,xyc); // c(FF000000) v(1) 
GD:= point(0.,xyc); // c(FF000000) v(1) 
GE:= segment(GA,GB); // c(FF000000) v(1) l(0) 
GG:= segment(GB,GC); // c(FF000000) v(1) l(0) 
GH:= segment(GC,GD); // c(FF000000) v(1) l(0) 
GI:= segment(GD,GA); // c(FF000000) v(1) l(0) 
GJ:= midpoint(GE); // c(FF000000) v(1) 
GK:= midpoint(GG); // c(FF000000) v(1) 
GL:= midpoint(GH); // c(FF000000) v(1) 
GM:= midpoint(GI); // c(FF000000) v(1) 
GN:= point(xn,yn); // c(FF000000) v(1) 
GO:= segment(GN,GM); // c(FF000000) v(1) l(0) 
GP:= segment(GN,GJ); // c(FF000000) v(1) l(0) 
GQ:= segment(GN,GK); // c(FF000000) v(1) l(0) 
GR:= segment(GN,GL); // c(FF000000) v(1) l(0) 
"

define:
a:=(x1,y1,x2,y2,x3,y3,x4,y4)->(ABS(x1*y2+x2*y3+x3*y4+x4*y1-x2*y1-x3*y2-x4*y3-x1*y4))/2 // shoelace formula for 4 points

xyc -- x and y coordinates of point C
xn -- x coordinate of point N
yn -- y coordinate of point N

initially, {xyc,xn,yn}:={10,3,6} // just a guess

   

use fsolve with 3 equations for areas 1, 2, and 3; and 3 unknowns {xyc,xn,yn}:

{xyc,xn,yn}:=fsolve({(a(0,(xyc/2),xn,yn,(xyc/2),xyc,0,xyc)) = 16,(a(0,0,(xyc/2),0,xn,yn,0,(xyc/2))) = 20,(a((xyc/2),0,xyc,0,xyc,(xyc/2),xn,yn)) = 32},{xyc,xn,yn},{10,3,6})

   

area 4 = 28

-road