Question

Using heron's formula find the area of an equilateral triangle of side 2a units

Answer 1

Answer:

We know

Using heron's formula

area of equilateral triangle = root 3/4 side square

So root 3/4 2a square = root 3/4 ×4a

Answer : Root 3a square

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\therefore{\text{Area\:of\:triangle=1.732a}^{2}\:units^{2}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{ \underline \bold{Given : }} \\ : \implies \text{Sides \: of \: triangle =2a units,2a units,2a units} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Area \: of \: triangle = ?}$

• According to given question :

$\bold{As \: we \: know \: that \: herons \: formula} \\ : \implies s = \frac{a + b + c}{2} \\ \\ : \implies s = \frac{2a+ 2a+ 2a}{2} \\ \\ : \implies s = \frac{6a}{2} \\ \\ \green{ : \implies s = 3a} \\ \\ \circ\: \bold{Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{3a(3a- 2a)(3a-2a)(3a- 2a)} \\ \\ : \implies \text{Area \: of \: triangle =}\sqrt{3a\times a\times a\times a} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{3a^{4}} \\ \\ : \implies \text{Area \: of \: triangle =}1.732a^{2}\: units^{2} \\ \\ \ \green{\therefore \text{Area \: of \: triangle = 1.732a}^{2}\: {units}^{2} }$