ANSWER:

Now,

Now,Area of Triangle = ½ × BASE × height

Now,Area of Triangle = ½ × base × heightHere, base = a, and height = h

Now,Area of Triangle = ½ × base × heightHere, base = a, and height = hNow, apply Pythagoras Theorem in the triangle.

Now,Area of Triangle = ½ × base × heightHere, base = a, and height = hNow, apply Pythagoras Theorem in the triangle.A2 = h2 + (a/2)2

Now,Area of Triangle = ½ × base × heightHere, base = a, and height = hNow, apply Pythagoras Theorem in the triangle.a2 = h2 + (a/2)2⇒ h2 = a2 – (a2/4)

Now,Area of Triangle = ½ × base × heightHere, base = a, and height = hNow, apply Pythagoras Theorem in the triangle.a2 = h2 + (a/2)2⇒ h2 = a2 – (a2/4)⇒ h2 = (3A2)/4

Now,Area of Triangle = ½ × base × heightHere, base = a, and height = hNow, apply Pythagoras Theorem in the triangle.a2 = h2 + (a/2)2⇒ h2 = a2 – (a2/4)⇒ h2 = (3a2)/4Or, h = ½(√3a)

Now,Area of Triangle = ½ × base × heightHere, base = a, and height = hNow, apply Pythagoras Theorem in the triangle.a2 = h2 + (a/2)2⇒ h2 = a2 – (a2/4)⇒ h2 = (3a2)/4Or, h = ½(√3a)Now, put the value of “h” in the area of the triangle equation.

Now,Area of Triangle = ½ × base × heightHere, base = a, and height = hNow, apply Pythagoras Theorem in the triangle.a2 = h2 + (a/2)2⇒ h2 = a2 – (a2/4)⇒ h2 = (3a2)/4Or, h = ½(√3a)Now, put the value of “h” in the area of the triangle equation.Area of Triangle = ½ × base × height

Now,Area of Triangle = ½ × base × heightHere, base = a, and height = hNow, apply Pythagoras Theorem in the triangle.a2 = h2 + (a/2)2⇒ h2 = a2 – (a2/4)⇒ h2 = (3a2)/4Or, h = ½(√3a)Now, put the value of “h” in the area of the triangle equation.Area of Triangle = ½ × base × height⇒ A = ½ × a × ½(√3a)

Now,Area of Triangle = ½ × base × heightHere, base = a, and height = hNow, apply Pythagoras Theorem in the triangle.a2 = h2 + (a/2)2⇒ h2 = a2 – (a2/4)⇒ h2 = (3a2)/4Or, h = ½(√3a)Now, put the value of “h” in the area of the triangle equation.Area of Triangle = ½ × base × height⇒ A = ½ × a × ½(√3a)Or, Area of Equilateral Triangle = ¼(√3a2)