Question

1.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
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Now,
Semi Perimeter=24/2
                         = 12cm
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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

Hi !
Perimeter = 24 cm

Perimeter of an equilateral triangle = 3a , where a = side

3a = 24

a = 8 cm

Semi perimeter = S = 8+8+8/2 = 12

Heron's formula :-

√s(s-a)(s-b)(s-c) 

a = b = c = 8 cm 


= √12(12-8)(12-8)(12-8)
= √12×4×4×4
= 16√3 cm²


The area of the equilateral triangle is 16√3 cm²