Question

Each side of an equilateral triangle measures 8 cm. Find (i) the area of the triangle, correct to 2 decimal places, and (ii) the height of the triangle, correct to 2 places of decimal. Take $\sqrt{3}=1.732.$

Answer 1

Sides of triangle = a = 8 cm
​(i) Area of an equilateral triangle = $\frac{\sqrt{3}}{4}\times a^2$
$$\begin{gathered} =\frac{\sqrt{3}}{4}\times 8^2 \\ =\frac{\sqrt{3}}{4}\times 64 \\ =16\sqrt{3} \\ =16\times 1.732 \\ =27.71{\mathrm{cm}}^2 \end{gathered}$$

(ii )Height of triangle = $\frac{\sqrt{3}}{2}\times a$
$$\begin{gathered} =\frac{\sqrt{3}}{2}\times 8 \\ =4\sqrt{3} \\ =4\times 1.732 \\ =6.93\mathrm{cm} \end{gathered}$$