Question

if
the perimeter of an
equilatual triangle
is 60 cm
what is its area​

Answer 1

Answer:Perimeter of the given equilateral triangle = 60 cm.

Length of each of its sides =603cm=20cm. =(100×1.732)cm2=173.2cm2. Hence, the area of the given triangle is 173.2 cm2

Step-by-step explanation:

Answer 2

Diagram:

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

Given:

• Perimeter = 60 cm

To find:

⟶  Area = ?

Formulas used:

→ Perimeter of Equilateral Triangle = 3 × Side

$\rightarrow \sf{Area\:of\:Equilateral\:Triangle = \dfrac{\sqrt{3}}{4}a^{2} }$

Method:

Perimeter = 3 × Side

⇒ 60 = 3 × side

⇒ Side = 60 ÷ 3

∴ Side = 20 cm

Now let's find area.

$\sf{Area = \dfrac{\sqrt{3}}{4}a^2}\\\\\\\implies \sf{Area = \dfrac{\sqrt{3}}{4} \times 20^2}\\\\\\\implies \sf{Area= \dfrac{\sqrt{3}}{4} \times 20 \times 20}\\\\\\\therefore \boxed{\bf{Area = 100\sqrt{3} cm^{2} }}$

Learn more:

• An Equilateral Triangle has 3 equal sides.
• We know that Perimeter is the Sum of all sides.

∴ Perimeter of Equilateral Triangle = 3 × Side