List of top Quantitative Aptitude Questions on Geometry asked in CAT

In a triangle \(ABC , ∠ BCA =50°\). D and E are points on AB and AC, respectively, such that AD = DE. If F is a point on BC such that BD = DF, then \(∠ FDE\), in degrees, is equal to

Let ABCD be a parallelogram. The lengths of the side AD and the diagonal AC are 10 cm and 20 cm, respectively. If the angle \(∠ADC \) is equal to 30° then the area of the parallelogram, in sq. cm, is

The cost of fencing a rectangular plot is ₹ 200 per ft along one side, and ₹ 100 per ft along the three other sides. If the area of the rectangular plot is 60000 sq. ft, then the lowest possible cost of fencing all four sides, in INR, is

If a rhombus has area 12 sq cm and side length 5 cm, then the length, in cm, of its longer diagonal is

Suppose the length of each side of a regular hexagon ABCDEF is 2 cm. It T is the mid point of CD, then the length of AT, in cm, is

The sides AB and CD of a trapezium ABCD are parallel, with AB being the smaller side. P is the midpoint of CD and ABPD is a parallelogram. If the difference between the areas of the parallelogram ABPD and the triangle BPC is 10 sq cm, then the area, in sq cm, of the trapezium ABCD is

If the area of a regular hexagon is equal to the area of an equilateral triangle of side 12 cm, then the length, in cm, of each side of the hexagon is

Let D and E be points on sides AB and AC, respectively, of a triangle ABC, such that AD : BD = 2 : 1 and AE : CE = 2 : 3. If the area of the triangle ADE is 8 sq cm, then the area of the triangle ABC, in sq cm, is

A circle of diameter 8 inches is inscribed in a triangle ABC where ∠ABC = 90°. If BC = 10 inches then the area of the triangle in square inches is

A park is shaped like a rhombus and has area 96 sq m. If 40 m of fencing is needed to enclose the park, the cost, in INR, of laying electric wires along its two diagonals, at the rate of ₹125 per m, is

A park is shaped like a rhombus and has area 96 sq m. If 40 m of fencing is needed to enclose the park, the cost, in INR, of laying electric wires along its two diagonals, at the rate of ₹125 per m, is

Let D and E be points on sides AB and AC, respectively, of a triangle ABC, such that AD : BD = 2 : 1 and AE : CE = 2 : 3. If the area of the triangle ADE is 8 sq cm, then the area of the triangle ABC, in sq cm, is

A circle of diameter 8 inches is inscribed in a triangle ABC where ∠ABC = 90°. If BC = 10 inches then the area of the triangle in square inches is

The area of the region satisfying the inequalities \(|x|-y≤1,y≥0\) and \(y≤1\) is [This Question was asked as TITA]

The area of the region satisfying the inequalities \(|x|-y≤1,y≥0\) and \(y≤1\) is

With rectangular axes of coordinates, the number of paths from (1,1) to (8,10) via (4,6), where each step from any point (x, y) is either to (x, y+1) or to (x+1, y), is

Let T be the triangle formed by the straight line 3x + 5y - 45 = 0 and the coordinate axes. Let the circumcircle of T have radius of length L, measured in the same unit as the coordinate axes. Then, the integer closest to L is

In triangle ABC, ‘D’ and ‘E’ are two points on sides AB and AC, respectively such that DE is parallel to BC. If AD=16 cm, BD=(5x-16) cm, AE=2x cm and EC=(25-2x) cm, then find the value of ‘x’.

PQRS is a rhombus such that length of its each side is 30 cm. If PR=36 cm and QS=\(4\sqrt{x}\) cm then the length of each side of the rhombus (in terms of ‘x’) is:

In the given figure, ‘O’ is the centre of the semi-circle and ∠MON =48°, Find ∠MRP.

In triangle PQR, PM is perpendicular to QR. If ‘T’ is a point in between ‘Q’ and ‘M’ such that PT = \(5\sqrt3\) cm, PM = \(\sqrt{39}\) cm then find the value of PQ such that QM : TM = 5 : 2.

In the given figure, AB is the chord of the circle with centre ‘O’. A tangent AT is drawn at point ‘A’ so that angle BAT = 48°, then measure of angle ADB is :

In triangle PQR, the straight line parallel to side QR meets PQ and PR at points ‘A’ and ‘B’, respectively. If PA = BR, PQ = 36 cm and PB = 6 cm, then BR = ?