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

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

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.

Prove that the line segment obtained by joining the midpoints of the diagonals of a trapezium is parallel to the parallel sides of the trapezium.

A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF = 10^(-12) F). What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6?

The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half of the distance between the foci is ……

What is the area of the plates of a 2 F parallel plate capacitor given that the separation between the plates is 0.5 cm ?

Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.

Prove that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.