Prove that the medians of an equilateral triangle are equal.

Using the concept of slope,prove that medians of an equilateral triangle are perpendicular to the corresponding sides.

Prove that the area of an equilateral triangle is equal to sqrt3/4 a^(2) , where a is the side of the triangle.

Prove that the area of an equilateral triangle is equal to (sqrt(3))/4a^2, where a is the side of the triangle. GIVEN : An equilateral triangle A B C such that A B=B C=C A=adot TO PROVE : a r( A B C)=(sqrt(3))/4a^2 CONSTRUCTION : Draw A D_|_B Cdot

Prove that a median of an equilateral triangle is perpendicular to the corresponding side.

Prove that the angle opposite to the equal sides of an equilateral triangle are equal.

Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.

Prove that the area of an equilateral triangle described on a side of a right-angled isosceles triangle is half the area of the equilateral triangle described on its hypotenuse.

Prove that each angle of an equilateral triangle is 60^(0)

Prove that the area of the equilateral triangle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the equilateral triangles drawn on the other two sides of the triangle.

If l is the length of the median of an equilateral triangle, then what is its area?