USING HERONS FORMULA FIND THE AREA OF AN EQUILATERAL TRIANGLE WHOSE PERIMETER IS 24 CM. (TAKE ROOT 3=1.732)
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Answered by
25
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
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
Answered by
5
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.
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