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In an equilateral triangle, another equilateral triangle is drawn inside joining the mid-points of the sides of the given equilateral triangle and the process continues uptofive times. What is the ratio of the area of fourth triangle to that of sixth triangle? (Original triangle is counted as 1st triangle)
In an equilateral triangle, another equilateral triangle is drawn inside joining the mid-points of the sides of the given equilateral triangle and the process continues up to seven times. What is the ratio of the area of fourth triangle to that of seventh triangle?
A circle of maximum area is inscribed in the square. An equilateral triangle is inscribed in that circle and all the vertices of the triangle touch the circle. A triangle is formed by the joining of the midpoint of the sides of the equilateral triangle. Find the ratio of the area of the square and area of the triangle which is formed by midpoints.
An equilateral triangle of area 300 cm2 is cut from its three vertices to form a regular hexagon. Area of hexagon is what percent of the area of triangle?(Each side of the regular hexagon is 1/3 rd the original side of equilateral triangle)
Which of the following statement(s) given below is / are TRUE? A: Cost of fencing a park in the shape of rhombus at the rate of Rs. 24 / m is Rs. 720 if area of park is 96 cm2 and ratio of diagonals of the park is 3 : 4. B: Length of perpendicular from a vertex of an equilateral triangle to opposite side is 6√3 cm of area of triangle is 36√3 cm2. C: Perimeter of an equilateral triangle of area 49√3 cm2 is 42 cm.
Triangle XYZ is similar to triangle RST. Area of triangle XYZ is 2304 cm2 and area of triangle RST is 1296 cm2. If the longest side of the triangle XYZ measures 144 cm, then what will be the measure of the longest side of the triangle RST?
Calculate the number of equilateral triangle that can be produced by melting and recasting a metallic sphere having a radius equal in length to the side of equilateral triangle.  (The equilateral triangle and sphere are having uniform thickness and also there is no loss of material in melting and recasting).
.An equilateral triangle E1 which is having perimeter 72 sq.cm .By the mid points of the side of triangle E1 we can draw an equilateral triangle E2 find the area of  Triangle E2.  
One side of a triangle and a rectangle is the same. The third vertex of the triangle lies on the midpoint of the rectangle side opposite the common side. The rectangle sides are in the ratio 2 : 3 and the common side is the longer side of the rectangle.  What is the sin value of the angle between the common side and the equal side of the triangle?
The side of a square, the side of an equilateral triangle and the diameter of a circle are equal. Find the ratio between the area of square, the area of equilateral triangle and the area of circle?