In [1]:

    

import sympy
from sympy.abc import x,y,r
from sympy.solvers.solvers import nsolve
from sympy import sin


    

In [2]:

    

pi = 3.14159
f1 = 2*r*sin(x/2) - 5
f2 = 2*r*sin(y/2) - 8
f3 = x + y - pi
ang_1,ang_2,radius = nsolve((f1, f2, f3), (x,y,r), (1,1,1))
ang_1,ang_2,radius


    

    
Out[2]:





(mpf('1.1171978852963868'),
 mpf('2.0243921147036131'),
 mpf('4.7169933788311705'))

In [3]:

    

total_area = radius**2 * pi
total_area


    

    
Out[3]:





mpf('69.900460865034646')

In [4]:

    

segment_areas = radius**2 * ((ang_1 - sin(ang_1)) + (ang_2 - sin(ang_2)))
segment_areas


    

    
Out[4]:





mpf('29.900401822626527')

In [5]:

    

kite_area = total_area - segment_areas
kite_area


    

    
Out[5]:





mpf('40.000059042408118')

In [6]:

    

from math import sqrt


    

In [7]:

    

radius = 13
width = 5


    

In [8]:

    

height = sqrt(radius**2 - width**2)


    

In [9]:

    

area = height * width
area


    

    
Out[9]:





60.0