Question

using herons formula find the area of an equilateral triangle whose perimeter is 24cm

Answer 1

we know that the sides of an equilateral Triangle are equal.

given he perimeter of the equilateral Triangle = 24cm

therefore side × 3 = 24cm

==> side = 24/3

==> side = 8cm

hence, all sides of the equilateral Triangle is 8cm.

let the sides of the triangle be a, b and c.

according to heron's formula, we have to first find it's semi-perimeter.

semi-perimeter of the triangle = 24/2 = 12cm

area of the triangle by heron's formula = √s(s-a)(s-b)(s-c)

= √12(12-8)(12-8)(12-8)

= √12×4×4×4

= √768

= (2 × 2 × 2)√6

= 16√3 cm²

the area of the equilateral Triangle is 16√3 cm²

HOPE THIS HELPS..!!

Answer 2

hope it is right for you guy

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