Question

Each side of an equilateral triangle measures 8 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. $(Take\sqrt{3}=\mathrm{1.732.})$

Answer 1

Area of equilateral triangle of side a = $\frac{\sqrt{3}}{4}\times a^2$

Here side a = 8 cm

Area of equilateral triangle = $\frac{\sqrt{3}}{4}\times 8^2$ = 27.71 $c{m}^2$
area = $\frac{1}{2}$ × b × h = 27.71
$\frac{1}{2}$ × 8 × h = 27.71
h = $\frac{27.71}{4}$
h = 6.92 cm