Question

find the area of an equilateral triangle whose each side is 8 cm long.
a) 6√
${3}cm^{2}$
b) 8√
${3}cm^{2}$
c) 16√
${3}cm^{2}$
d) none of this​

Answer 1

Answer:

• Option (c) 16√3 cm² is the required answer.

Step-by-step explanation:

According to the Question

It is given that,

• Length of side Equilateral triangle ,s = 8cm

we have to calculate the area of equilateral triangle .

As we know area of Equilateral triangle is calculated by

Area of Equilateral triangle = √3/4 × Side²

substituting the value we get

↠Area of Equilateral triangle = √3/4 × 8²

↠Area of Equilateral triangle = √3/4 × 64

↠ Area of Equilateral triangle = √3 × 16

↠Area of Equilateral triangle = 16√3 cm²

• Hence , the area of equilateral triangle is 16√3 cm².

Additional Information !!

$\begin{gathered}\boxed{\begin {array}{cc}\\ \quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}$

Answer 2

Given : Side of the Equilateral triangle is 8 cm .

To Find : Find the Area of Triangle

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SolutioN :

$\maltese$ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ Area{\small_{(Equilateral \; Triangle )}} = \dfrac{ \sqrt{3}}{ 4 } \times \bigg( Side \bigg)^{2} }}}}}$

$\maltese$ Calculating the Area :

$\begin{gathered} \qquad \; \implies \; \; \sf { Area = \dfrac{ \sqrt{3}}{ 4 } \times \bigg( Side \bigg)^{2} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \implies \; \; \sf { Area = \dfrac{ \sqrt{3}}{ 4 } \times \bigg( 8 \bigg)^{2} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \implies \; \; \sf { Area = \dfrac{ \sqrt{3}}{ 4 } \times 64 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \implies \; \; \sf { Area = \dfrac{ \sqrt{3}}{ \cancel4 } \times \cancel{64} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \implies \; \; \sf { Area = \sqrt{3} \times 16 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \implies \; \; {\underline{\boxed{\pmb{\pink{\sf{ Area = 16 \sqrt{3} \; {cm}^{2} }}}}}} \; {\purple{\bigstar}} \\ \\ \\ \end{gathered}$

$\qquad \; \red\leadsto$ Area of this Triangle is 16√3 cm² .

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