the height of an equilateral triangle is 6 CM then find the measure of its side
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Answer:
The area of an equilateral triangle is 20.78 cm²
Step-by-step explanation:
Height of an equilateral triangle = 6 cm
✓3/2 × Side = 6
Side = 6×2/✓3
Side = 12/✓3 × ✓3/✓3 = 12✓3/3 = 4✓3 cm
Length of each side of an equilateral∆ = 4✓3 cm.
S = 1/2× (side+Side+Side)
S = 1/2 × (3×4✓3)
S = 1/2 × 12✓3 = 6✓3 cm
∴ ,
(S-a) = (6✓3 - 4✓3) = 2✓3
(S-b) = (6✓3 - 4✓3) = 2✓3
(S-c) = (6✓3 - 4✓3) = 2✓3
So , by herons formula, we have:
Area = ✓S(S-a)(S-b)(S-c) cm²
= ✓6✓3(2✓3)(2✓3)(2✓3)
= ✓6✓3 × 8 × 3✓3
=> ✓6✓3 × 24✓3 = ✓144 × 3
=> ✓432 = 20.78 cm²
Hence,
The area of an equilateral triangle is 20.78 cm²
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