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 Reply
Answer:
oahdhbdjcidne
Step-by-step explanation:
hsgebfjcioenskxoowibanxooc
Given,
To Find,
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