Respuesta :

As here we are given with an equilateral triangle, whose side is 3 cm, and we need to find the height and area of the equilateral triangle. So, for this let's recall that, the area of any equilateral triangle with side a is given by ;

  • [tex]{\boxed{\bf{Area_{(Equilateral\:\: Triangle)}=\dfrac{\sqrt{3}}{4}a^{2}}}}[/tex]

So, if we substitute a = 3, in our Formula, it will yield to

[tex]{:\implies \quad \sf Area_{(Equilateral\:\:Triangle)}=\dfrac{\sqrt{3}}{4}(3)^{2}}[/tex]

[tex]{:\implies \quad \sf Area_{(Equilateral\:\:Triangle)}=\dfrac{\sqrt{3}}{4}(9)}[/tex]

[tex]{:\implies \quad \boxed{\bf{Area_{(Equilateral\:\:Triangle)}=\dfrac{9\sqrt{3}}{4}\:\:cm^{2}}}}[/tex]

Now, as we know that, for any triangle we also have a formula that is ;

  • [tex]{\boxed{\bf{Area_{(Triangle)}=\dfrac{1}{2}\times Base\times Height}}}[/tex]

Now, Here as the triangle is equilateral, so it's base will just be same 3, and if we let height be H, so we will be having

[tex]{:\implies \quad \sf \dfrac{1}{2}\times 3\times H=\dfrac{9\sqrt{3}}{4}}[/tex]

[tex]{:\implies \quad \sf H=\dfrac{9\sqrt{3}}{4}\times \dfrac23}[/tex]

[tex]{:\implies \quad \boxed{\bf{Height=\dfrac{3\sqrt{3}}{2}\:\:cm}}}[/tex]

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