Mathematics Question and Solution
Calculating Area of the yellow Hexagon.
Let x be the side length of the hexagon.
a²+3² = x²
a = √(x²-9) cm.
b² = 2x²-2x²cos120
b = √(3x²)
b = √(3)x cm.
It implies;
Calculating x.
sinc = √(x²-9)/x --- (1).
sinc = 5/(√(3)x) --- (2).
Equating (1) and (2).
√(x²-9)/x = 5/(√(3)x)
Cross Multiply.
5x = √(3)x*√(x²-9)
5 = √(3x²-27)
25 = 3x²-27
3x² = 52
x² = 52/3
x = √(52/3)
x = 4.16333199893 cm.
Again, x is the side length of the yellow hexagon.
Recall.
b = √(3)x cm.
And x = √(52/3) cm.
b = √(3)*√(52/3)
b = √(52) cm
It implies;
Area yellow hexagon is;
2(½*√(52/3)²sin120)+(√(52)*√(52/3))
= ((52/3)*½√(3))+⅓(52√(3))
= ⅙(52√(3))+⅓(52√(3))
= ⅙(52√(3)+104√(3))
= ⅙(156√(3))
= 26√(3) cm²
