a)
[tex]d = 9 cm \\d = a\sqrt{2} \\a\sqrt{2} = 9 \\a = \frac{9}{\sqrt{2} } \\a = \frac{9\sqrt{2} }{2} \\a = 4,5\sqrt{2} (cm) \\P = a^2\\P = (4,5\sqrt{2})^2 = 20,25 * 2 = 40,5 (cm^2)[/tex]
Odp.: Pole danego kwadratu wynosi 40,5 cm².
b)
[tex]P = 72 cm^2\\P = a^2\\a^2 = 72 \\a = \sqrt{72} \\a = 6\sqrt{2} (cm)\\d = ?\\d = a\sqrt{2} \\d = 6\sqrt{2} * \sqrt{2} = 6 *2 = 12 (cm)\\[/tex]
Odp.: Długość przekątnej danego kwadratu wynosi 12 cm.
