Mathematics Question and Solution
Calculating x, the length that form tangents of the two semi circles.
x²+2²=6²
x²=36-4
x²=32
x = √(32) cm.
x = 4√(2) cm.
Therefore;
Area blue is;
Area trapezium with two parallel length 2 cm and 4 cm, and height 4√(2) cm - Area triangle with two length 4 cm each and angle atan(2√(2)) - Area triangle with two length 2 cm each and angle (90+ atan(1/(2√(2)))
= ½(2+4)*4√(2) - ½(4²)sin(atan(2√(2))) - ½(2²)sin(90+ atan(1/(2√(2))))
= 12√(2) - 7.54247233266 - 1.88561808316
= 7.5424723326 cm²
Or
Area blue is;
Area triangle with height √(32-32cos(atan(2√(2))) cm and base √(8-8cos((90+ atan(1/(2√(2))))) cm
= ½*√(32-32cos(atan(2√(2)))*√(8-8cos((90+ atan(1/(2√(2)))))
= ½*√(64/3)*√(32/3)
= ½*√(2048/9)
= ½*⅓*32√(2)
= ⅓(16√(2)) cm²
= 7.54247233266 cm²
