Mathematics Question and Solution
Calculating square area.
tana = (k+2k)/k
a = atan(3)°
b = 90-a
b = atan(⅓)°
tanc = 3k/2k
c = atan(3/2)°
d = 180-a-c
d = 180-atan(3)-atan(3/2)
d = 52.1250163489°
e = 180-a
e = (90+atan(⅓))°
f = 180-e-b
f = 180-(90+atan(⅓))-atan(⅓)
f = (90-2atan(⅓))°
f = 53.1301023542°
g = 180-f-d
g = 180-(90-2atan(⅓))-52.1250163489
g = 74.7448812969°
h² = (3k)²+k²
h = √(10)k units.
(2k/sin(53.1301023542)) = (j/sin(90+atan(⅓)))
j = 2.37170824512k units.
l = h-j
l = 0.79056941504k units.
(0.79056941504k/sin74.7448812969) = (m/sin52.1250163489)
m = 0.6468295214k units.
Calculating k.
0.5*m*l*sin53.1301023542 = 3
0.40909090909k² = 6
k² = 6/0.40909090909
k² = 14.6666666667
k = 3.82970843103 units.
Notice.
Square side length is;
3k
= 3*3.82970843103
= 11.4891252931 units.
Therefore, square area is;
(3k)²
= 11.4891252931²
= 132 square units.
