In an equilateral triangle with side a, prove that,
the altitude is of length `(sqrt(3))/(2)a`.

In an equilateral triangle with side a, prove that, the area of the triangle (sqrt(3))/(4)a^(2) .

Draw an equilateral triangle whose sides are 5.2 cm. each

ABC is an equilateral triangle of side 2a. Find each of its altitude.

The base of an equilateral triangle with side 2a lies along the Y-axis such that the mid-point of the base is at the origin. Find vertices of the triangle.

In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitude.

Three sphere of masses m_,m andm_ are located at the vertices of an equilateral triangle having side of same length. Find the moment of inertia of the system about one of side of triangle.

Prove that the area of the equilateral triangle described on the side of a square is half the area of the equilateral triangles described on its diagonal.

An equilateral triangle has each of its sides of length 4 cm. If (x_(r),y_(r)) (r=1,2,3) are its vertices the value of |{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|^2

In the given figure, ABC is an equilateral triangle with side 14 cm and a circle of radius 7 cm is drawn with vertex A as centre. Find the area of the shaded region. (Use sqrt(3) = 1.73 ) [Hint : Required area = Area of triangle + Area of circle -2 xx Area of sector]

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.