Question

The height of an equilateral triangle is 6 cm. Its area is
(a) $12\sqrt{3}{\mathrm{cm}}^2$
(b) $6\sqrt{3}{\mathrm{cm}}^2$
(c) $12\sqrt{2}{\mathrm{cm}}^2$
(d) 18 cm²

Answer 1

(a) $12\sqrt{3}{\mathrm{cm}}^2$
$$\begin{gathered} \mathrm{Height}\mathrm{of}\mathrm{equilateral}\mathrm{triangle}=\frac{\sqrt{3}}{2}\times \mathrm{Side} \\ \Rightarrow 6=\frac{\sqrt{3}}{2}\times \mathrm{Side} \\ \Rightarrow \mathrm{Side}=\frac{12}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}=\frac{12}{3}\times \sqrt{3}=4\sqrt{3}\mathrm{cm} \\ \mathrm{Now}, \\ \mathrm{Area}\mathrm{of}\mathrm{equilateral}\mathrm{triangle}=\frac{\sqrt{3}}{4}\times (\mathrm{Side}{)}^2 \\ =\frac{\sqrt{3}}{4}\times {\left(4\sqrt{3}\right)}^2 \\ =\frac{\sqrt{3}}{4}\times 48 \\ =12\sqrt{3}{\mathrm{cm}}^2 \end{gathered}$$