Zad 1.
Wzór na wysokość -> h = [tex]\frac{a\sqrt{3} }{2}[/tex]
Wzór na pole -> P = [tex]\frac{a^{2}\sqrt{3} }{4}[/tex]
a) h = 5√3
a = [tex]\frac{2\sqrt{3}h }{3}[/tex]
a = [tex]\frac{2\sqrt{3}*5\sqrt{3} }{2}[/tex]
a = 15
P = [tex]\frac{15^{2}\sqrt{3} }{4}[/tex]
P = [tex]\frac{225{}\sqrt{3} }{4}[/tex]
b) h = 3√15
a = [tex]\frac{2\sqrt{3}h }{3}[/tex]
a = [tex]\frac{2\sqrt{3}*3\sqrt{15} }{2}[/tex]
a = 9√5
P = [tex]\frac{(9\sqrt{5}) ^{2}\sqrt{3} }{4}[/tex]
P = [tex]\frac{405{}\sqrt{3} }{4}[/tex]
c) h = [tex]\frac{1}{2}[/tex]
a = [tex]\frac{2\sqrt{3}h }{3}[/tex]
a = [tex]\frac{2\sqrt{3}*\frac{1}{2} }{2}[/tex]
a = [tex]\frac{1}{2}[/tex][tex]\sqrt{3}[/tex]
P = [tex]\frac{(\frac{1}{2} \sqrt{3}) ^{2}\sqrt{3} }{4}[/tex]
P = [tex]\frac{3{}\sqrt{3} }{16}[/tex]
Zad. 2
Wzór na wysokość -> h = [tex]\frac{a\sqrt{3} }{2}[/tex]
Wzór na pole -> P = [tex]\frac{a^{2}\sqrt{3} }{4}[/tex]
a) P = 25√3
25√3 = [tex]\frac{a^{2}\sqrt{3} }{4}[/tex]
100√3 = a²√3
a² = 100
a = 10
h = [tex]\frac{a\sqrt{3} }{2}[/tex]
h = [tex]\frac{10\sqrt{3} }{2}[/tex]
h = 5√3
b) P = √3
√3 = [tex]\frac{a^{2}\sqrt{3} }{4}[/tex]
4√3 = a²√3
a² = 4
a = 2
h = [tex]\frac{a\sqrt{3} }{2}[/tex]
h = [tex]\frac{2\sqrt{3} }{2}[/tex]
h = √3
c) P = [tex]\frac{\sqrt{3} }{4}[/tex]
[tex]\frac{\sqrt{3} }{4}[/tex] = [tex]\frac{a^{2}\sqrt{3} }{4}[/tex]
√3 = a²√3
a² = 1
a = 1
h = [tex]\frac{a\sqrt{3} }{2}[/tex]
h = [tex]\frac{1\sqrt{3} }{2}[/tex]
h = [tex]\frac{\sqrt{3} }{2}[/tex]