The area of a trapezium is 418.5 cm2 and the distance between its parallel sides is 27 cm. If one of the parallel sides is of length 23 cm, find the length of the other side.
From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 5 cm, 7 cm and 3 cm. Find the area of the triangle.
The diameter of a solid metallic right circular cylinder is equal to its height. After cutting out the largest possible solid sphere ^@S^@ from the cylinder, the remaining material is recast to form a solid sphere ^@S_1^@. What is the ratio of the radius of the sphere ^@S^@ to that of sphere ^@S_1 ?^@
Nuwan draws ^@4^@ cards out of a deck of ^@52^@ cards. What is the probability that he draws ^@a \space 7, \space a \space 9, \space a \space King, \space and \space a \space Jack^@?