Question

Q5. Prove that the area of equilateral triangle is equal to cube 34 a 2 where a is the side of the triangle.​

Answer 1

⇒Since all the 3 sides of the triangle are same

AB = BC = CA = a

⇒Draw a perpendicular from point A to base BC, AD ⊥⊥ BC

By using Pythagoras theorem

In △ ADC

h² = AC² - DC²

= a² - (a/2)² [Because, DC = a²]

= a²- a²/4

h = √3a/2

⇒Area of a triangle = 1/2 * Base * Height

= 1/2 * a * 3√a/2

= √3/4*a²

⇒The area of a equilateral triangle = √3/4*a²

Answer 2

Answer:

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