In a quadrilateral ABCD, \(\angle A = 32^\circ\) and \(\angle B = 58^\circ\). The bisectors of \(\angle C\) and \(\angle D\) meet at O. What is the measure of \(\angle DOC\)?

Consider an equilateral quadrilateral whose angle bisectors intersect at right angles. One side of the quadrilateral measures 10 cm, and one of its perpendicular diagonals is 12 cm. Find half of the area of the quadrilateral.

In a parallelogram ABCD, the diagonals intersect at O. ∠BCA = 38° and ∠CAB = 27°. Find ∠AOD if ∠ADO : ∠CDO = 2 : 3.

In quadrilateral PQRS, ∠P = 105°, ∠Q = 65° and ∠R = ∠S. Find the measure of 2∠P + ∠S − ∠Q.

In a trapezium ABCD, AB∥CD and AB = 16 cm, CD = 8 cm. What is the ratio of the areas of ΔABC and ΔACD?

If E and F are the mid-points of the two non-parallel sides AD and BC of the trapezium ABCD, in which AB ∥ CD, then find EF = ?

The area of a rhombus is \(48\text{ cm}^2\) and the length of one of its diagonals is \(12\sqrt{2}\text{ cm}\). What is the length of each side of this rhombus?

The side length of a rhombus is \(\frac{17}{3}\text{ cm}\) and one of its diagonals is \(\frac{16}{3}\text{ cm}\). Find the length of the other diagonal.

The four angles of a quadrilateral are in the ratio \(3 : 4 : 5 : 6\). What is the value of the smallest angle?

The ratio between the length and breadth of a rectangular park is 3 : 2. If a man cycling along the boundary at the speed of 12 km per hour completes one round in 8 minutes, then the area of the park in square meter will be

The side of a rhombus is 26 cm. The length of one of its diagonals is 20 cm. The sum of the lengths of the diagonals of this rhombus is equal to the perimeter of a rectangle. If the difference between the length and breadth of the rectangle is 6 cm, then what is the area of the rectangle?

PQRS is a cyclic quadrilateral. If ∠P is 4 times ∠R, and ∠S is 3 times ∠Q, then the average of ∠Q and ∠R is:

ABCD is a trapezium in which AB || DC and DC is perpendicular to BC. If ∠DAB = 110°, then ∠ABC - ∠ADC =_____.