Mathematics Question and Solution
a+a+b = 20
2a+b = 20 --- (1).
20² = c²+10²
c² = 400-100
c = = √(300)
c = 10√(3) units.
It implies;
a+b = c
a+b = 10√(3) --- (2).
Solve (1) and (2) simultaneously, Calculating a and b.
dSubtracting (2) from (1).
2a+b = 20 -- (1)
a+b = 10√(3) -- (2)
a = 20-10√(3)
a = 2.6794919243 units.
It implies;
From (2).
a+b = 10√(3)
b = 10√(3)-a
b = 10√(3)-2.6794919243
b = 14.6410161514 units.
It implies;
Area Blue is;
Area square with diagonal 14.6410161514 units + 4(Area sector with radius 20 units and angle 30° - Area triangle with height 20 units and base 20sin30 units).
= ½(14.6410161514)²+4((30π*20*20/360)-(0.5*20*20sin30))
= 107.1796769728+4(104.7197551197-100)
= 107.1796769728+4(4.7197551197)
= 107.1796769728+18.8790204788
= 126.0586974516 square units.
