Each side of an equilateral triangle is 10 cm.

(i) The area of the equilateral triangle $=\frac{\sqrt{3}}{4} \times \operatorname{side}^{2}$

$=\frac{\sqrt{3}}{4} \times 10^{2}$

$=\frac{\sqrt{3}}{4} \times 100$

$=25 \sqrt{3} \mathrm{~cm}^{2}$

or $25 \times 1.732=43.3 \mathrm{~cm}^{2}$

So, the area of the triangle is $25 \sqrt{3} \mathrm{~cm}^{2}$ or $43.3 \mathrm{~cm}^{2}$.

(ii) As, area of the equilateral triangle $=25 \sqrt{3} \mathrm{~cm}^{2}$

$\Rightarrow \frac{1}{2} \times$ Base $\times$ Height $=25 \sqrt{3}$

$\Rightarrow \frac{1}{2} \times 10 \times$ Height $=25 \sqrt{3}$

$\Rightarrow 5 \times$ Height $=25 \sqrt{3}$

$\Rightarrow$ Height $=\frac{25 \sqrt{3}}{5}=5 \sqrt{3}$

or height $=5 \times 1.732=8.66 \mathrm{~m}$

$\therefore$ The height of the triangle is $5 \sqrt{3} \mathrm{~cm}$ or $8.66 \mathrm{~cm}$.