Question

USING HERONS FORMULA FIND THE AREA OF AN EQUILATERAL TRIANGLE WHOSE PERIMETER IS 24 CM. (TAKE ROOT 3=1.732)

Answer 1

perimeter = 24cm
side = 24/3= 8cm

herons formula--- root of {s(s-a)(s-b)(s-c)}
s = (a+b+c)/2
s= 24/2= 12

area : root of {s(s-a)(s-b)(s-c)}
= root of { 12(12-8)(12-8)(12-8)}
= root of ( 12*4*4*4)
=root of (768)
= √3*√256
= 1.732*16 = 27.712 cm

Hence the area of this triangle is 27.712

Answer 2

Answer:

Heron's formula for calculation of Area of an triangle →

✓s(s-a)(s-b)(s-c)

Where, s= Semi-perimeter and a,b and c are sides of Triangle respectively.

So here , all sides are equal and each side = Perimeter/3 (As Triangle it Equilateral and formula for perimeter for triangle is 3×side and for side it'll be Perimeter/3)

= 24/3

= 8cm

Semi perimeter = 24/2 = 12cm

Now apply the Heron's formula →

✓12(12-8)(12-8)(12-8)

= ✓12×4×4×4

= ✓2×2×2×2×2×2×2×2×3

= 2×2×2×2×✓3

= 16✓3 cm²

Answer→ The area of Equilateral Triangle with side 8 cm is 16✓3 cm².