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1. Find the area of a quadrilateral whose one of the diagonals is 50 m and the lengths of perpendiculars from the other two vertices are 29 m and 21 m respectively.
2. The interior angle of a regular polygon is 135°, then find the number of sides of the polygon.
3. A man by walking diametrically across a circular grass plot, finds that it has taken him 45 seconds less than if he had kept to the path around the outside. If he walks 90 metres per minute, find the circumference of the grass plot.
4. Three metal cubes with edges 6 cm, 8 cm and 10 cm respectively, are melted together and formed into a single cube. Find the diagonals of this new cube.
5. Find the volume of the prism if the base is a triangle with sides 54 m, 72 m and 90 m and the height is 12 m.