List of top Quantitative Aptitude Questions on Geometry asked in CAT

A rectangle $ABCD$ has sides $AB = 45 \, \text{cm}$ and $BC = 26 \, \text{cm}$. Point $E$ is the midpoint of side $CD$. Find the radius of the incircle of the triangle $\triangle AED$.

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

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 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

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 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

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

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

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

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

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

Points E, F, G, H lie on the sides AB, BC, CD, and DA, respectively, of a square ABCD. If EFGH is also a square whose area is 62.5% of that of ABCD and CG is longer than EB, then the ratio of length of EB to that of CG is

The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar is

The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is

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

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 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.