Rhombus of side 6 cm has an angle equal to the external angle of a regular octagon. Find the area of the rhombus.

A circle inscribed in a square of side 2 has an equilateral triangle inscribed inside it. What is the ratio of areas of the equilateral triangle to that of the square?

An acute-angled isosceles triangle has two of its sides equal to 10 and 16. Find the area of this triangle.

Three equal circles are placed inside an equilateral triangle such that any circle is tangential to two sides of the equilateral triangle and to two other circles. What is the ratio of the areas of one circle to that of the triangle?

 There is an equilateral triangle with a square inscribed inside it. One of the sides of the square lies on a side of the equilateral ?. What is the ratio of the area of the square to that of the equilateral triangle?