Question:
Each side of an equilateral triangle measures $8 \mathrm{~cm}$. Find
(i) the area of the triangle, correct to 2 places of decimal and
(ii) the height of the triangle, correct to 2 places of decimal. Take $\sqrt{3}=1.732$.
Solution:
Side of the equilateral triangle = 8 cm
(i)
Area of equilateral triangle $=\frac{\sqrt{3}}{4} \times(\text { Side })^{2}$
$=\frac{\sqrt{3}}{4} \times(8)^{2}$
$=\frac{1.732 \times 64}{4}$
$=27.71 \mathrm{~cm}^{2}$
(ii)
Height $=\frac{\sqrt{3}}{2} \times$ Side
$=\frac{\sqrt{3}}{2} \times 8$
$=\frac{1.732 \times 8}{2}$
$=6.93 \mathrm{~cm}$