ГДЗ по геометрии 8 класс Атанасян Задание 502

\[\boxed{\mathbf{502.ОК\ ГДЗ - домашка\ на}\ 5}\]

\[Рисунок\ по\ условию\ задачи:\]

\[\mathbf{Дано:}\]

\[\text{ABCD} - параллелограмм;\]

\[P_{\text{ABCD}} = 42\ см;\]

\[\text{BH} = 4\ см;\]

\[\text{BF} = 5\ см.\]

\[\mathbf{Найти:}\]

\[S_{\text{ABCD}} - ?\]

\[\mathbf{Решение.}\]

\[1)\ P_{\text{ABCD}} = 2\text{AB} + 2\text{AD} =\]

\[= 2\left( \text{AB} + \text{AD} \right) = 42\ см.\]

\[\text{AB} + \text{AD} = 21\ см \Longrightarrow\]

\[\Longrightarrow \text{AB} = 21 - \text{AD}.\]

\[2)\ S_{\text{ABCD}} = \text{BH} \bullet \text{AD} = \text{BF} \bullet \text{CD} =\]

\[= \text{BF} \bullet \text{AB}.\]

\[4 \bullet \text{AD} = 5 \bullet \left( 21 - \text{AD} \right)\]

\[4\text{AD} = 105 - 5\text{AD};\]

\[9\text{AD} = 105\]

\[\text{AD} = \frac{105}{9} = 11\frac{6}{9} = 11\frac{2}{3}\ см.\]

\[3)\ S_{\text{ABCD}} = 4 \bullet 11\frac{2}{3} = 44\frac{8}{3} =\]

\[= 46\frac{2}{3}\ см^{2}.\]

­\(\mathbf{Ответ:}46\frac{2}{3}\ см^{2}\mathbf{.}\)