Question

Find the height of an equilateral triangle having side 4cm ?​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Given,

• The Side of Equilateral Triangle = 4cm

To Find,

• The Height of Equilateral Triangle.

Solution,

The Perimeter of Equilateral Triangle (P)= 3A

→ The Perimeter of Equilateral Triangle = 3(4cm)

→ The Perimeter of Equilateral Triangle = 12cm

Semi Perimeter of Equilateral Triangle (S) = P/2

→ Semi Perimeter of Equilateral Triangle = 12cm/2

→ Semi Perimeter of Equilateral Triangle = 6cm

Area = Heron's Formula

→ Area = √[S × (S - A) × (S - A) × (S - A)]

→ Area = √[6 × (6 - 4) × (6 - 4) × (6 - 4)]cm²

→ Area = √[6 × 2 × 2 × 2]cm²

→ Area = 2√[3 × 2 × 2]cm²

→ Area = 2 × 2√3cm²

→ Area = 4√3cm²

Area = ½ × B × H

→ 4√3cm² = ½ × 4cm × H

→ 4√3cm² = 2cm × H

→ 4√cm²/2cm = H

→ Height = 2√3cm

Required Answer,

The Height of Equilateral Triangle is 2√3cm