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

ABC is a right angled triangle, having lfloorB=90^(@) . If BD=DC , Show that AC^(2)=4AD^(2)-3AB^(2) OR Prove that area of the equilateral triangle described on the side of a square is half the area of the equilateral triangle described on its diagonal.

Prove that ara of the equilateral triangle described on the sides of square is half the area of the equilateral triangle described on its diagonal.

Prove that the area of the euilateral traingle described on the side of a square is half the area of the equilatiral triangle described on it's square . OR In Delta ABC D,E, F are the midpoints of te sides BC, AC and AB respectively. Find the rations of the areas of Delta DEF Delta ABC

Prove that an equilateral triangle can be constructed on any given line segment.

Prove that the ratio of the area of a circle and the equilateral triangle whose side is equal to the diameter of the circle is pi:sqrt3

Derive the formula for height and area of an equilateral triangle.

The altitude of an equilateral triangle having the length of its side 12 cm is

Draw an equilateral triangle whose sides are 5.2 cm. each

Three coins of unit radius are placed in an equilateral triangle as shown in the following figure. The area of that equilateral triangle is :

Prove that if the area of similar triangles are equal, they are congruent.