I am from std8 . I have question ofsubject mathematics . Question is-By using Heron's formula to find the area of an equilateral triangle whose side is 'p'.( I need it urgently)
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Given: An equilateral triangle whose side is p.
Area of the triangle by using heron's formula=root[(s-a)(s-b)(s-c)]
Let 2s=perimeter
or,2s=p+p+p
or,2s=3p
or,s=3p/2
Now,area=root[(3p/2-p)(3p/2-p)(3p-p)]
=root[(3p-2p)/2×(3p-
2p)/2×(3p-2p)/2]
=root[p/2×p/2×p/2]
p/2×root(p/2)
Hence area of triangle is p/2×root(p/2).
Area of the triangle by using heron's formula=root[(s-a)(s-b)(s-c)]
Let 2s=perimeter
or,2s=p+p+p
or,2s=3p
or,s=3p/2
Now,area=root[(3p/2-p)(3p/2-p)(3p-p)]
=root[(3p-2p)/2×(3p-
2p)/2×(3p-2p)/2]
=root[p/2×p/2×p/2]
p/2×root(p/2)
Hence area of triangle is p/2×root(p/2).
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