Question

area of an equilateral triangle with side 43 cm using heron's formula​

Answer 1

Answer:

Step-by-step explanation:

Heron's formula = √s(s-a)(s-b)(s-c)

S= a+b+c/2 = 43+43+43/2 =64.5

S-a = 64- 43 = 21

S-b = 64- 43 = 21

S-c = 21

Putting values

Area of ∆ = √64.5(21)(21)(21)

= 21√64.5 × 21

= 21√1354.5

Further √1354.5 = 36.8

So ar(∆) = 21 × 36.8 = 772.8

Or you can leave it in the root form only

Answer 2

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

$\green{\therefore{\text{Area\:of\:triangle=800.64\:cm}^{2}}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Sides \: of \: triangle = 43 cm,43 cm,43 cm} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Area \: of \: triangle = ?}$

• According to given question :

$\bold{As \: we \: know \: that \: herons \: formula} \\ : \implies s = \frac{a + b + c}{2} \\ \\ : \implies s = \frac{43+ 43+ 43}{2} \\ \\ : \implies s = \frac{129}{2} \\ \\ \green{ : \implies s = 64.5} \\ \\ \circ\: \bold{Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{64.5(64.5- 43)(64.5-43)(64.5- 43)} \\ \\ : \implies \text{Area \: of \: triangle =}\sqrt{64.5\times 21.5 \times 21.5\times 21.5} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{641025.1875} \\ \\ : \implies \text{Area \: of \: triangle =}800.64\: cm^{2} \\ \\ \ \green{\therefore \text{Area \: of \: triangle = 800.64\:{cm}}^{2} }$