Sir Mike Ambrose is the author of the question.
Area purple exactly in decimal is;
Area triangle with height 5cm and base 7.5cm - Area triangle with height 3cm and base 7.5cm - Area triangle with side 2cm and 1.89765856604cm, and angle at an(3/2)° - Area triangle with side 4.26973177358cm and 4.84664832643cm, and angle (at an(⅔)-atan(2/5))°
= ½(5*(15/2)) - ½(3*(15/2)) - ½(2*1.89765856604)sin(atan(3/2)) - ½(4.26973177358*4.84664832643)sin(atan(⅔)-atan(2/5))
= 7.5 - 1.57894736843 - 2.13157894737
= 3.7894736842 cm²
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