Question

Find the area of an equilateral triangle whose sides are of 14 cm each using Heron's Formula

Answer 1

Hi friend...


The sides are of 14 cm;-

Semi perimeter-- a+b+c
______

2


= 14+14+ 14/2

=42/2

=21

_________________
√ 21[21-14) (21-14) (21-14)

=21×7×7×7 (do prime factorisation)

=3×7×7×7×7(make pair of two)

=3×7×7

=147 answer....


Thanks...♌

Hope it is helpful ✨✨✨

Answer 2

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

$\green{\therefore{\text{Area\:of\:triangle=84.87\:cm}^{2}}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Sides \: of \: triangle = 14 cm,14 cm,14 cm} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Area \: of \: triangle = ?}$

• According to given question :

$\bold{As \: we \: know \: that \: herons \: formula} \\ : \implies s = \frac{a + b + c}{2} \\ \\ : \implies s = \frac{14+ 14+ 14}{2} \\ \\ : \implies s = \frac{42}{2} \\ \\ \green{ : \implies s = 21} \\ \\ \circ\: \bold{Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{21(21- 14)(21-14)(21- 14)} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{21 \times 7\times 7\times 7} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{7203} \\ \\ : \implies \text{Area \: of \: triangle =}84.87 \: cm^{2} \\ \\ \ \green{\therefore \text{Area \: of \: triangle = 84.87 {cm}}^{2} }$