Предмет: Геометрия, автор: vladislava009

Помогите пожалуйста!  Найти площадь заштрихованной части.
 нижняя сторона треугольника совпадает с диаметром окружности

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Автор ответа: Мilkа
0
1) Так как угол ABC опирается на полуокружность AC, то этот угол равен 90'.
Значит треугольник ABC-прямоугольный и угол BAC=30'. Из этого следует, что гипотенуза AC (диаметр окружности)=2*4=8 см.
2) Найдем AB по теореме Пифагора: 
AB^2=AC^2-BC^2=64-16=48 \ AB=4 sqrt{3}
3) Sabc= frac{1}{2} AB*BC= frac{1}{2}*4 sqrt{3} *4=8 sqrt{3} cm^2
4) Радиус-половина диаметра. Значит R=4 см.
5) S круга= pi R^2=3,14*16=50,24 cm^2
6) S закрашенной части=Sкруга - S треугольника=50,24- 4sqrt{3} =~43,31 см^2
Мой ответ: ~43,31 см^2
Если неверно - удаляйте....

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