Question

if an equilateral triangle has a perimater of 24 cm , then find the area of the triangle​

Answer 1

Answer:
16√3cm²

Step-by-step explanation:

Given,
Perimeter of an equilateral △ = 24cm

•Each side of the △ = 8 cm.

now consider: 8 as 'a',
then,

Area of an equilateral △ is √3a²/4
so,

=√3x8²/4
=√3x64/4
=√3x16
=16√3cm²

Area of an equilateral △ with perimeter 24cm= 16√3cm²

Answer 2

${\huge{\mathfrak{ \red{Solution \: - }}}}$

Let a be the side of triangle.

Perimeter of triangle = 24cm

Since the triangle is equilateral .

$\sf \: Perimeter \: = 3a$

$\therefore \sf \: a = \dfrac{24}{3}$

$\sf \: a = 8cm$

Now

${\implies \sf \: Area \: of \: equilateral \: triangle = \dfrac{ \sqrt{3} }{4} {a}^{2} }$

${\implies \sf \: Area \: of \: triangle = \dfrac{1.732}{4} \times 8 \times 8}$

${ \blue{ \boxed{ \blue{ \boxed{ \blue { \tt \dag \: Area = 27.712 \: \dag}}}}}}$