Question

using herons formula calculate the area and the altitude of an equilateral triangle of side 80 cm.√3=1.73

Answer 1

Step-by-step explanation:

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Answer 2

Altitude of triangle is 40√3  cm

Area of triangle is 1600√3 cm²

Given:

Side of the equilateral triangle = 80 cm.

To find:

Calculate the area and the altitude of an equilateral triangle

Solution:

As we know the formula Heron's formula for area of triangle is given by

Area of triangle = √(s(s-a)(s-b)(s-c)

As we know sides of equilateral triangle are equal

Area of equilateral triangle =√(s(s-a)(s-a)(s-a) = √s(s-a)³  

S = semi perimeter of triangle = 3a/2 = 240/2 = 120 cm

Therefore,

Area of triangle = √120(120 - 80)³ = √120(40)³ = √12(640000)

= 800√4×3 = 1600√3

Area of triangle = 1600√3 cm²

Altitude of triangle h = (½) × √3 × s  [ where s is side of triangle ]

=  (½) × √3 × 80

= 40√3  cm

Altitude of triangle = 40√3  cm

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