Question

If the perimeter of an equilateral triangle is 36 cm , calculate its are and height.
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Answer 1

$\mathfrak \blue { \underline{ \underline{here \: is \: your \: answer : }}} \\ perimeter \: of \: an \: equilateral \: traingle \: = 3a \\ p = 3a \\ 36 = 3a \\ a = \frac{36}{3} \\ a = 12 \\ so..area \: of \: a \: equilateral \: traingle \: is \: = \frac{ \sqrt{3} }{4} {a}^{2} \\ \\ a = \frac{ \sqrt{3} }{4} \times 12 \times 12 \\ a = 36 \sqrt{3} c {m}^{2}$

Height of the triangle is 2√2cm

Hope my answer will help you..

Answer 2

GIVEN :-

• Perimeter of an equilateral triangle is 36 cm

TO FIND :-

• Area and height of the equilateral triangle

SOLUTION :-

Perimeter of a equilateral triangle is given by ,

$\large{\underline {\boxed{ \bigstar{ | { \sf{ \: P = 3a}}}}}}$

Where ,

• a is side of the equilateral triangle

We have ,

• Perimeter of equilateral triangle as 36 cm

$\implies \sf \: 3a = 36 \\ \\ \implies \sf \: a = \frac{36}{3} \\ \\ \implies {\underline {\boxed {\pink{\sf {\: a = 12}}}}}$

Area of equilateral triangle is given by ,

$\large {\underline {\boxed {\bigstar {\sf{ \: A= \frac{ \sqrt{3} }{4} {a}^{2} }}}}}$

$\implies \sf \: A = \frac{ \sqrt{3} }{4} (12) {}^{2} \\ \\ \implies \sf \: A = \frac{ \sqrt{3} }{4} (144) \\ \\ \implies \sf \: A = \sqrt{3} (36) \\ \\ \implies {\underline{ \boxed {\blue {\sf{A = 36 \sqrt{3} \: cm {}^{2} }}}}}$

Height of an equilateral triangle is given by ,

$\large {\underline {\boxed {\bigstar {\sf{ \: H= \frac{ \sqrt{3}a }{2} }}}}}$

$\implies \sf \: H = \frac{ \sqrt{3} (12)}{2} \\ \\ \implies \sf \: H= \frac{ \sqrt{3}( \cancel{12}) }{ \cancel{2}} \\ \\ \implies \sf \: H = \sqrt{3} (6) \\ \\ \implies {\underline {\boxed {\blue{ \sf{H = 6 \sqrt{3} \: cm}}}}}$

∴ The height and area of the given equilateral triangle are $\large\sf{6\sqrt{3}}$ cm and $\large\sf{36\sqrt{3}}$ cm²