Prove that the area of a trapezium is half the sum of the parallel sides multiplied by the distance between them.

Find by integration the area of the trapezoid bounded by y=4x=-3,y=0 and x=3 .Verify your result by finding the area of a trapezoid as the product of half the sum of the two parallel sides and the distance between them.

Prove that the area of a rhombus is half the area of the rectangle produced by the diagonals of the rhombus.

Prove that the area of a rhombus is equal to half of the product of the diagonals.

Prove that the slant sides of a cyclic trapezium are equal.

By vector method prove that the straight line joining the mid-points of the diagonals of a trapezium is parallel ot the parallel sides and half of their difference.

Prove by vector method that the line segment joining the mid-points of the diagonals of a trapezium is parallel to the parallel sides and equal to half of their difference.

What will be the effect on the capacity of a parallel plate capacitor when the area of each plate is doubled and the distance between them is also doubled?

Using vector properties, show that, a straight line obtained by joining the mid-points of the oblique sides of a trapezium is parallel to the parallel sides of the trapezium and is equal to half of the sum of lengths of the parallel sides.

Equilateral triangles are drawn on the three sides of a right angled triangle. Show that the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides.