Cześć!
Wzór na pole trójkąta równobocznego o boku a
[tex]\text{P}=\frac{a^2\sqrt3}{4}[/tex]
a)
[tex]a=8 \ cm\\\\\text{P}=\frac{8^2\sqrt3}{4}=\frac{64\sqrt3}{4}=\boxed{16\sqrt3 \ cm^2}[/tex]
b)
[tex]a=10 \ cm\\\\\text{P}=\frac{10^2\sqrt3}{4}=\frac{100\sqrt3}{4}=\boxed{25\sqrt3 \ cm^2}[/tex]
c)
[tex]a=2\sqrt3 \ cm\\\\\text{P}=\frac{(2\sqrt3)^2\cdot\sqrt3}{4}=\frac{2^2\cdot(\sqrt3)^2\cdot\sqrt3}{4}=\frac{4\cdot3\cdot\sqrt3}{4}=\boxed{3\sqrt3 \ cm^2}[/tex]
d)
[tex]a=5\sqrt2 \ cm\\\\\text{P}=\frac{(5\sqrt2)^2\cdot\sqrt3}{4}=\frac{5^2\cdot(\sqrt2)^2\cdot\sqrt3}{4}=\frac{25\cdot2\cdot\sqrt3}{4}=\frac{50\sqrt3}{4}=\boxed{12,5\sqrt3 \ cm^2}[/tex]
