Mathematics Question and Solution
Radius of the ascribed quarter circle is;
1+1 = 2 cm.
a² = 1²+2²
a = √(5) cm.
Observing similar plane shape (right-angled) side length ratios.
√(5) - 4
1 - b
Cross Multiply.
b = ⅕(4√(5)) cm.
c²+b² = a²
c² = √(5)²-(⅕(4√(5)))²
c² = 5-(80/25)
c = ⅕√(45) cm.
Therefore, area inscribed green quadrilateral is;
Area triangle with height 1 cm and base 2 cm + Area triangle with height ⅕(4√(5)) cm and base ⅕√(45) cm.
(½*1*2)+(½*⅕√(45)*⅕(4√(5)))
= 1+ ⅕(6)
= 2⅕ cm²
= 2.2 cm²
