Question

1.Using Heron,s formula find the area of an equilateral triangle whose perimeter is 24 cm.

Answer 1

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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Answer 2

Given,
Perimeter= 24 cm

∴ let the side of an equilateral triangle be x
We know that the perimeter of an equilateral triangle = 3 x side 
∴ 24 = 3x
⇒x =8cm
=====================
Now,
Semi Perimeter=24/2
                         = 12cm
====================
Now ,
Using Herons 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

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∴ The area of the equilatral triangle is 16√3 cm²