3) Find the area of an equilateral triangle one of whose sides measure a cm, using heron’s formula
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Given,
The length of each sides of the equilateral triangle = a cm
To find,
The area of the given equilateral triangle by using Heron's formula.
Solution,
To calculate the area of the given equilateral triangle by using Heron's formula we have calculate the semiperimeter of the given equilateral triangle.
Semiperimeter (s) = (3×a)/2 = 3a/2 cm
[Equilateral triangle has three same sized sides.]
Area :
= ✓{3a/2 × (3a/2 - a) × (3a/2 - a) × (3a/2 - a)}
= ✓(3a/2 × a/2 × a/2 × a/2)
= ✓(3a⁴/4)
= ✓3a²/2 cm²
Hence, the area of the given equilateral triangle is ✓3a²/2 cm².
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