Question

Find the area of an equilateral triangle whose perimeter is 180cm​

Answer 1

Answer:

$1558.8 {cm}^{2}$

Step-by-step explanation:

P= 180

P = 3x

3x = 180

x = 180/3

x = 60

Area =

$\sqrt{3} \div 4 \times {x}^{2}$

Hence

$\sqrt{3} = 1.732$

1.732×3600÷4

1.732×900

173.2×9

1558.8cm^2

$1558.8 {cm}^{2}$

Answer 2

Answer:

900√3 (or) 1558.8 cm²

Step-by-step explanation:

Perimeter of equilateral triangle = 180 cm

=> 3a = 180

=> a = 60 cm

Semi-perimeter s = (a + b + c)/2

=> (60 + 60 + 60)/2

=> 180/2

=> 90 cm

Area = √s(s - a)(s - b)(s - c)

        = √90(90 - 60)(90 - 60)(90 - 60)

       = √90 * 30 * 30 * 30

       = √2430000

      = 900√3

     = 1558.8 cm²

Hope it helps!