Question

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

Answer 1

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

Answer 2

let the side of triangle be xcm.
3x=24cm
x=8cm
s=24/2cm=12cm
by using herons formula,
√12(12-8)(12-8)(12-8)
=√12*4*4*4
=√2*2*3*2*2*2*2*2*2
=2*2*2*2√3
=16√3cm²
HOPE IT HELPS YOU.