Question

If the length of a side of an equilateral triangle is 3 root 3 cm then find the area perimeter and height of that side

Answer 1

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

$\bold{Area, \ perimeter \ and \ height \ are }$

$\bold{6.75\sqrt3 \ cm^{2}, \ 9\sqrt3 \ cm \ and \ 4.5 \ cm \ respectively.}$

$\bold\orange{Given:}$

$\bold{=>Side \ of \ a \ equilateral \ triangle}$

$\bold{=3\sqrt3 \ cm}$

$\bold\pink{To \ find:}$

$\bold{=>Area}$

$\bold{=>Perimeter}$

$\bold{=>Height}$

$\bold\green{\underline{\underline{Solution}}}$

$\bold{Area \ of \ equilateral \ triangle}$

$\bold{=\frac{\sqrt3}{4}×side^{2}}$

$\bold{=\frac{\sqrt3}{4}×(3\sqrt3)^{2}}$

$\bold{=\frac{27\sqrt3}{4}}$

$\bold{=6.75\sqrt3 \ cm^{2}}$

__________________________________

$\bold{Perimeter \ of \ equilateral \ triangle}$

$\bold{=3×side}$

$\bold{=3×3\sqrt3}$

$\bold{=9\sqrt3 \ cm}$

__________________________________

$\bold{Height \ of \ an \ equilateral \ triangle}$

$\bold{=\frac{\sqrt3}{2}×side}$

$\bold{=\frac{\sqrt3}{2}×3\sqrt3}$

$\bold{=\frac{9}{2}}$

$\bold{=4.5 \ cm}$

$\bold\purple{\tt{\therefore{Area, \ perimeter \ and \ height \ are }}}$

$\bold\purple{\tt{6.75\sqrt3 \ cm^{2}, \ 9\sqrt3 \ cm \ and \ 4.5 \ cm \ respectively.}}$