Wzory
Wysokość
[tex] \boxed{ \frac{a \sqrt{3} }{2} }[/tex]
Pole
[tex] \boxed{ \frac{ {a}^{2} \sqrt{3} }{4} }[/tex]
Obliczmy długość jednego boku
[tex]150 \sqrt{3} cm = 3a | \div 3 \\ \bold{a = 50 \sqrt{3} cm}[/tex]
Zatem wysokość
[tex] \frac{a \sqrt{3} }{2} = \frac{50 \sqrt{3} \times \sqrt{3} }{2} = \frac{50 \times 3}{2} = \frac{150}{2 } = \\ = \boxed{75 cm}[/tex]
Pole
[tex] \frac{ {a}^{2} \sqrt{3} }{4} = \frac{( {50 \sqrt{3})^{2} } \sqrt{3} }{4} = \frac{2500 \times 3 \times \sqrt{3} }{4} = \frac{7500 \times \sqrt{3} }{4} = \\ = \boxed{1875 \sqrt{3}{cm}^{2} }[/tex]
