X, Y and Z are three equilateral triangles. The sum of the areas of X and Y is equal to the area of Z. If the side lengths of X and Y are 6 cm and 8 cm respectively, then what is the side length of Z?

If the area of a square is equal to the area of an equilateral triangle, the ratio of the side of the square and the side of the equilateral triangle is

A triangle has side lengths x cm, x + 31 cm and x + 26 cm. If its area is 126 square cm, then what is the value of x ?

The perimeter and the area of a right-angled triangle are 36 cm and 54 square cm respectively. What is the length of the hypotenuse ?

ABC is a triangle with sides AB = 41 cm, BC = 28 cm and CA = 15 cm. If D, E and F are the mid-points of AB, BC and CA respectively, then what is the area of the triangle DEF?

Two parallel sides of a trapezium are 29 cm and 21 cm. Non-parallel sides are equal and each is of length 8.5 cm. What is the area of the trapezium?