Question

find the area of an equilateral triangle whose perimeter is 18 cm .also find the height

Answer 1

Perimeter of equilateral triangle=sum of all sides
18=3{side}
18÷3=side
Side=6
Then,area of equilateral triangle=√3/4(side×side)
Area=9√4

Answer 2

Answer:

$Height \: of \: equilateral \\triangle\\ (h) = 3\sqrt{3}\:cm$

Step-by-step explanation:

$Let\: side \: of \: an \: equilateral \: triangle = a \:cm$

$Perimeter \: of \: an\: equilateral triangle \\(P) = 18 \: cm\: [Given ]$

$\implies 3a =18\: [given ]$

$\implies a=\frac{18}{3}$

$\implies a =6 \:cm$

$We\: know \: that \\</p><p>Height \: of \: equilateral \\triangle\\ (h) = \frac{\sqrt{3}}{2}\times a$

$\implies h = \frac{\sqrt{3}}{2}\times 6\\=3\sqrt{3}\:cm$

Therefore,

$Height \: of \: equilateral \\triangle\\ (h) = 3\sqrt{3}\:cm$

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