Question

if the perimeter of an equilateral triangle is 360 cm. Then its area will be​

Answer 1

Answer:

$\huge \ast\bold { \underline{ \underbrace{ \underline {\textsf{ \pink{given:-}}}}}} \ast$

The perimeter of an equilateral triangle = 360 cm

$\huge \ast\bold { \underline{ \underbrace{ \underline {\textsf{ \orange{To \:find:-}}}}}} \ast$

Area of the equilateral triangle=?

$\huge \ast\bold { \underline{ \underbrace{ \underline {\textsf{ \blue{Formula:-}}}}}} \ast$

$\bold \blue{ \: \: \: \: \: 3a \implies \: perimeter}$

$\begin{gathered}\bold\rm\purple \frac{\sqrt{3}}{4} a² \\ \sf\end{gathered}$

$\huge \ast\bold { \underline{ \underbrace{ \underline {\textsf{ \red{Diagram:-}}}}}} \ast$

$\setlength{ \unitlength}{1cm} \\ {picture}(0,0) \thicklines \qbezier(1,0)(1,0)(3,3) \qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf C }\put(5.2,-0.3){ \bf B }\end{picture}$

$\huge \ast\bold { \underline{ \underbrace{ \underline {\textsf{ \pink{Concept}}}}}} \ast$

As provided in the given Question , First we will find the perimeter by 3a=> perimeter . In here it is 3a because as it is an equilateral triangle the sides are same ,(a) and the sides are three . So it is 3a.

Then we would find the area by the 2nd formula provided in the formula list.

$\huge \ast\bold { \underline{ \underbrace{ \underline {\textsf{ \purple{Solution:-}}}}}} \ast$

➟ 360 = 3a

➟ a = 360/3

➟ 120 = a

Using the 2nd formula :

$Area = \begin{gathered}\rm \frac{\sqrt{3}}{4}(120)²\\ \sf \end{gathered}$

$Area = \rm \frac{\sqrt{3}}{\cancel4} × \cancel{120}$

$Area = \rm \sqrt{3}× 30 × 120$

$Area = \rm 3600 \sqrt{3}cm.3600$

Answer 2

$\huge\orange{\overbrace{\red{\underbrace {\color {pink}{{\red\:{❥Question}}}}}}}$

If the perimeter of an equilateral triangle is 360 cm. Then its area will be?

$\huge\orange{\overbrace{\red{\underbrace {\color {pink}{{\red\:{❥Answer}}}}}}}$

$\red{✦Given:}$

✎Perimeter of Equilateral triangle is 360 cm

$\underline\red{✦Formula:-}$

${✎Perimeter = 3a}$

$\blue{▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂}$

$➾\: 360 = 3 a$

$➾ \: a \: = \frac{360}{3}$

$➾ \: a \: = 120 \: cm$

✧Now, side of equilateral triangle is 120cm

$\underline\red{✦Formula:-}$

$✎Area = \frac{ \sqrt{3} }{4} \times a {}^{2}$

$\blue{▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂}$

$➾\: \frac{ \sqrt{3} }{4} \times (120) {}^{2}$

$➾ \: \sqrt{3} \times 30 \times 120$

$➾ \: 3600 \sqrt{3} \: cm {}^{3}$

$\red{✦Hence,\:Area\: is\:3600√3 \: cm ²}$

$\huge\orange{❥Thank\:You.!}$