Question

For an equilateral triangle of side 6cm, find the area of the triangle without using heron's formula.

Answer 1

Let the triangle be ABC.

The side of the triangle = 6cm

Make a perpendicular on BC from A and let it be D.

Since it is an equilateral triangle

triangles ADC and ADB are right angled triangles and BD=DC=3cm.

Now by Pythagoras theorem

${AC}^2$ = ${AD}^2$ + ${DC}^2$ $\Rightarrow$ AD = $\sqrt{(25-9)}$ = 4cm

Now area of triangle ADC = $\frac{1}{2}$ $\times$ base $\times$ height = $\frac{1}{2}$ $\times$ 3 $\times$ 4 =6${cm}^2$

Area of triangle ABC = 2 $\times$ Area of triangle ADC = 2 $\times$ 6 = 12${cm}^2$