Question

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

Answer 1

Answer:

✏Perimeter : 360 cm

✏formula to calculate perimeter : 3 × side

✏applying Formula : 3 × s => 360

: s => 360 / 3

: s => 120 cm

✏120 cm is a side of an equilateral triangle...

✏then , Area of the equilateral ∆ is 3600√3cm.

Hope it helps you dear.......

❤ _ ❤ _ ❤

Answer 2

$\huge { \boxed{ \sf{ \red{ Question:-}}}}$

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

$\huge { \boxed{ \sf{ \orange{ Answer:-}}}}$

Area of the equilateral triangle is 3600√3 cm.

$\huge { \boxed{ \sf{ \green{ Explanation:-}}}}$

$\large{ \underline {\sf {\purple{Given:- }}}}$

• Perimeter of equilateral triangle is 360cm.

$\large{ \underline {\sf {\purple{To \: Find:-}}}}$

• Area of equilateral triangle.

$\large{ \underline {\sf {\purple{Understanding:-}}}}$

As we know the formula for finding perimeter of equilateral triangle is:-

$\sf{perimeter = sum \: of \: all \: sides}$

So, we will find all sides(that are always equal) by using this formula.

$\implies \sf{p = 3s}$

Where,

• 3s = 3 equal sides of triangle
• p = perimeter

$\implies \sf{360= 3s}$

$\implies \sf{ \frac{360}{3} = s}$

$\implies \sf{ 120 = s}$

So, the equal sides of triangle are 120cm.

Diagram:-

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

$\large{ \underline {\sf {\purple{Syncing:-}}}}$

Formula for finding the area of equilateral triangle is

$\sf {Area =  {\sf{\begin{gathered}\rm \frac{\sqrt{3}}{4} s²\\\sf\end{gathered}}}}$

Now, let's put all the values.

$\sf {Area =  {\sf{\begin{gathered}\rm \frac{\sqrt{3}}{4} 120²\\\sf\end{gathered}}}}$

$\implies \sf area ={\sf{\begin{gathered}\rm\frac{\sqrt{3}}{4} 120 \times 120\\\sf\end{gathered}}}$

$\implies \sf area = \sqrt{30} \times 30 \times 120$

$\implies \sf area = 3600 \sqrt{3} cm$

So, the area of equilateral triangle is 3600√3 cm.