wzór na pole kwadratu z przekątnej:
[tex]P=\frac{d^{2}}{2}[/tex]
długość boku a to √ z pola, a obwód to a · 4
[tex]a) \\d = 15\sqrt{2} cm\\P= \frac{(15\sqrt{2})^{2} }{2} = \frac{225\cdot 2}{2} = 225cm^{2}\\a = \sqrt{225cm^{2}} = 15cm\\obw =15cm \cdot 4 = 60cm[/tex]
[tex]b)\\d = 7\sqrt{6} dm\\P = \frac{(7\sqrt{6})^{2}}{2} = \frac{49\cdot 6}{2} = (49 \cdot 3) dm^{2}\\a=\sqrt{49 \cdot 3dm^{2}} = 7\sqrt{3} dm\\obw=7\sqrt{3} dm \cdot 4 = 28\sqrt{3} dm[/tex]
[tex]c) \\d=10mm\\P=\frac{10^{2}}{2} = \frac{100}{2}= 50mm^{2}\\a = \sqrt{50mm^{2}} = \sqrt{2\cdot 25mm^{2}} = 5\sqrt{2} mm\\obw = 5\sqrt{2} mm \cdot 4 = 20\sqrt{2} mm[/tex]
[tex]d)\\d = 2\sqrt{3} cm\\P = \frac{(2\sqrt{3})^{2}}{2} = \frac{4\cdot 3}{2} = \frac{12}{2} = 6cm^{2}\\a= \sqrt{6cm^{2}} = \sqrt{6} cm\\obw = \sqrt{6} cm \cdot 4= 4\sqrt{6} cm[/tex]
