Question:
Each side of an equilateral triangle measure 8 cm. The area of the triangle is
(a) $8 \sqrt{3} \mathrm{~cm}^{2}$
(b) $16 \sqrt{3} \mathrm{~cm}^{2}$
(c) $32 \sqrt{3} \mathrm{~cm}^{2}$
(d) $48 \mathrm{~cm}^{2}$
Solution:
(b) $16 \sqrt{3} \mathrm{~cm}^{2}$
Area of equilateral triangle $=\frac{\sqrt{3}}{4} \times(\text { Side })^{2}$
$=\frac{\sqrt{3}}{4} \times(8)^{2}$
$=\frac{\sqrt{3}}{4} \times 64$
$=16 \sqrt{3} \mathrm{~cm}^{2}$