Question

The height of an equilateral triangle is 4v3 cm. Find its area correct to three decimal
places. (Take 3 = 1.732)​

Answer 1

Answer:

$\boxed{\bf \: Area\:of\:an\:equilateral\:triangle= \: 27.712 \: {cm}^{2} \: }$

Step-by-step explanation:

Let assume that side of an equilateral triangle be x cm

Given that,

$\sf \: Height\:of\:an\:equilateral\:triangle = 4 \sqrt{3} \:cm$

$\sf \: \dfrac{ \sqrt{3} }{2} \times side = 4 \sqrt{3} \:$

$\sf \: \dfrac{ \sqrt{3} }{2} \times x = 4 \sqrt{3} \:$

$\sf \: x = 4 \sqrt{3} \times \dfrac{2}{ \sqrt{3} } \:$

$\sf \: x = 4 \times 2\:$

$\implies\sf \: x = 8 \: cm$

Now,

$\sf \:Area\:of\:an\:equilateral\:triangle$

$\sf \: = \: \dfrac{ \sqrt{3} }{4} \times {x}^{2}$

$\sf \: = \: \dfrac{1.732 }{4} \times {(8)}^{2}$

$\sf \: = \: \dfrac{1.732 }{4} \times 64$

$\sf \: = \: 1.732 \times 16$

$\sf \: = \: 27.712 \: {cm}^{2}$

Hence,

$\implies\boxed{\bf \: Area\:of\:an\:equilateral\:triangle= \: 27.712 \: {cm}^{2} \: }$

$\rule{190pt}{2pt}$

Formulae Used:

$\sf \: Height\:of\:an\:equilateral\:triangle = \dfrac{ \sqrt{3} }{2} \times side \:$

$\sf \:Area\:of\:an\:equilateral\:triangle = \dfrac{ \sqrt{3} }{4} \times {(side)}^{2} \:$