Mathematics Question and Solution
Calculating Area Yellow.
Notice.
8 units is the side length of the regular heptagon.
a = ⅐*180(7-2)
a = ⅐(900)°
a is the single interior angle of the regular heptagon.
b² = 8²+8²-2*8*8cos(900/7)
b = 14.4155018864 units.
c = ½(180-(900/7))
c = 25.714285°
d = (900/7)-c
d = (900/7)-25.714285
d = 102.857143571°
e² = 14.4155018864²+4²-2*14.4155018864*4cos102.857143571
e = 15.7945782971 units.
(15.7945782971/sin102.857143571) = (4/sinf)
f = 14.2942589329°
g = c+f
g = 25.714285+14.2942589329
g = 40.0085439329°
h = 180-d-g
h = 180-102.857143571-40.0085439329
h = 37.1343124961°
(8/sin37.1343124961) = (j/sin40.0085439329)
j = (8sin40.0085439329)/sin37.1343124961
j = 8.51969189622 units.
It implies, area yellow is;
0.5*8*jsin102.857143571
= 0.5*8*8.51969189622sin102.857143571
= 33.2243416368 square units.
