Answer:
[tex]\sf\:\boxed{\bf\:Area_{(Equilateral\:triangle)} = 16\sqrt{3} \: {cm}^{2} \: } \\ [/tex]
Formulae Used:
[tex]\sf\:\boxed{\begin{aligned}& \qquad \:\sf \: Perimeter_{(Equilateral\:triangle)} = 3 \times side \qquad \: \\ \\& \qquad \:\sf \: Area_{(Equilateral\:triangle)} = \dfrac{ \sqrt{3} }{4} \times {(side)}^{2} \end{aligned}}[/tex]
Step-by-step explanation:
Let assume that side of an equilateral triangle be x cm.
Given that, Perimeter of an equilateral triangle is 24 cm.
[tex]\implies\sf\:3x = 24 \\ [/tex]
[tex]\implies\sf\:x = 8 \: cm \\ [/tex]
Now,
[tex]\sf\: Area_{(Equilateral\:triangle)} \\ [/tex]
[tex]\sf\: = \: \dfrac{ \sqrt{3} }{4} {x}^{2} \\ [/tex]
[tex]\sf\: = \: \dfrac{ \sqrt{3} }{4} \times {(8)}^{2} \\ [/tex]
[tex]\sf\: = \: \dfrac{ \sqrt{3} }{4} \times 8 \times 8 \\ [/tex]
[tex]\sf\: = \: \sqrt{3} \times 2 \times 8 \\ [/tex]
[tex]\sf\: = \: 16\sqrt{3} \\ [/tex]
Hence,
[tex]\implies\sf\:\boxed{\bf\:Area_{(Equilateral\:triangle)} = 16\sqrt{3} \: {cm}^{2} \: } \\ [/tex]
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Answers & Comments
Answer:
Perimeter of equilateral triangle = 24 cm. Calculations: Let length of triangle be 'a'. .. Area of equilateral triangle is 16√3 cm2.
Verified answer
Answer:
[tex]\sf\:\boxed{\bf\:Area_{(Equilateral\:triangle)} = 16\sqrt{3} \: {cm}^{2} \: } \\ [/tex]
Formulae Used:
[tex]\sf\:\boxed{\begin{aligned}& \qquad \:\sf \: Perimeter_{(Equilateral\:triangle)} = 3 \times side \qquad \: \\ \\& \qquad \:\sf \: Area_{(Equilateral\:triangle)} = \dfrac{ \sqrt{3} }{4} \times {(side)}^{2} \end{aligned}}[/tex]
Step-by-step explanation:
Let assume that side of an equilateral triangle be x cm.
Given that, Perimeter of an equilateral triangle is 24 cm.
[tex]\implies\sf\:3x = 24 \\ [/tex]
[tex]\implies\sf\:x = 8 \: cm \\ [/tex]
Now,
[tex]\sf\: Area_{(Equilateral\:triangle)} \\ [/tex]
[tex]\sf\: = \: \dfrac{ \sqrt{3} }{4} {x}^{2} \\ [/tex]
[tex]\sf\: = \: \dfrac{ \sqrt{3} }{4} \times {(8)}^{2} \\ [/tex]
[tex]\sf\: = \: \dfrac{ \sqrt{3} }{4} \times 8 \times 8 \\ [/tex]
[tex]\sf\: = \: \sqrt{3} \times 2 \times 8 \\ [/tex]
[tex]\sf\: = \: 16\sqrt{3} \\ [/tex]
Hence,
[tex]\implies\sf\:\boxed{\bf\:Area_{(Equilateral\:triangle)} = 16\sqrt{3} \: {cm}^{2} \: } \\ [/tex]