Mathematics Question and Solution
tana = 5/8
a = atan(5/8)°
b = atan(8/5)°
c = 180-45-a
c = (135-atan(5/8))°
d = (135-atan(8/5))°
(e/sin(atan(8/5))) = (3/sin(135-atan(8/5)))
e = 2.6108558075 units.
(f/sin(atan(5/8))) = (6/sin(135-atan(5/8)))
f = 3.2635697593 units.
Area Green is;
(0.5*8*5)-(0.5*2*2)-(0.5*2.6108558075*3sin45)-(0.5*3.2635697593*6sin45)
= 20-2-2.7692307693-6.923076923
= 8.3076923077 square units.
Or
Area Green is;
0.5(3.2635697593+2.6108558075)*2√(2)
= √(2)(5.8744255668)
= 8.3076923077 square units.
g² = 2²+2²
g² = 8
g = 2√(2) units.
h² = 2(2√(2))²
h² = 16
h = 4 units.
j = 8-h-3
j = 1 unit.
Area Orange is;
(0.5*5*5)-(0.5*1*1)-(0.5*2√(2)*2√(2))
= 12.5-0.5-4
= 8 square units.
Or
k² = 2(1)²
k = √(2) units.
l² = 5²+5²
l = √(50)
l = 5√(2) units.
m = l-2√(2)
m = 3√(2) units.
It implies, orange area is;
0.5(√(2)+3√(2))*2√(2)
= √(2)(4√(2))
= 8 square units.
Therefore;
Orange Area : Green Area exactly in decimal is;
8÷8.3076923077
= 0.962962963
Orange Area : Green Area exactly in fraction is;
962/999
= 26/27
