ГДЗ по геометрии 9 класс Мерзляк Задание 154

\[Дано:\]

\[ABCD - параллелограмм;\]

\[MNFK - прямоугольник;\]

\[AB = MN;\]

\[AD = NF;\]

\[S_{\text{ABCD}} = \frac{1}{2}S_{\text{MNFK}}.\]

\[Найти:\]

\[\angle BAD.\]

\[1)\ S_{\text{MNFK}} = MN \bullet FK = AB \bullet AD.\]

\[2)\ S_{\text{ABCD}} = AB \bullet AD \bullet \sin{\angle BAD}\]

\[AB \bullet AD \bullet \sin{\angle BAD} = \frac{1}{2}AB \bullet AD\]

\[\sin{\angle BAD} = \frac{1}{2}\text{\ \ \ }\]

\[\angle BAD = 30{^\circ}.\]

\[Ответ:\ \ 30{^\circ}.\]