CAT: GeometryQuadrilaterals. Free, no login required.

ABCD is a trapezium in which AB is parallel to DC, AD is perpendicular to AB, and AB = 3DC. If a circle inscribed in the trapezium touching all the sides has a radius of 3 cm, then the area, in sq. cm, of the trapezium is

If the length of a side of a rhombus is 36 cm and the area of the rhombus is 396 sq. cm, then the absolute value of the difference between the lengths, in cm, of the diagonals of the rhombus is

In a rectangle ABCD, AB = 9 cm and BC = 6 cm. P and Q are two points on BC such that the areas of the figures ABP, APQ, and AQCD are in geometric progression. If the area of the figure AQCD is four times the area of triangle ABP, then BP : PQ : QC is

A quadrilateral $A B C D$ is inscribed in a circle such that $A B: C D=2: 1$ and $B C: A D=5: 4$. If $A C$ and $B D$ intersect at the point $E$, then $A E$ : $C E$ equals

The lengths of all four sides of a quadrilateral are integer valued. If three of its sides are of length $1$ cm, $2$ cm and $4$ cm, then the total number of possible lengths of the fourth side is

Let $ABCD$ be a parallelogram such that the coordinates of its three vertices $A, B, C$ are $(1, 1), (3, 4)$ and $(-2, 8)$, respectively. Then, the coordinates of the vertex $D$ are

A trapezium $ABCD$ has side $AD$ parallel to $BC$, $\angle$BAD = $90°$, $BC = 3$cm and $AD = 8$cm. If the perimeter of this trapezium is $36$cm, then its area, in sq. cm, is

Let $ABCD$ be a parallelogram. The lengths of the side $AD$ and the diagonal $AC$ a $10$ cm and $20$ cm, respectively. If the angle $\angle ADC$ is equal to $30^\circ$ 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

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

The sides $A B$ and $C D$ of a trapezium $A B C D$ are parallel, with $A B$ 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 $A B C D$ is

If a rhombus has area $12 \mathrm{sq} \mathrm{cm}$ and side length $5 \mathrm{~cm}$, then the length, in cm, of its longer diagonal is

In a trapezium $\mathrm{ABCD}, \mathrm{AB}$ is parallel to $\mathrm{DC}, \mathrm{BC}$ is perpendicular to DC and $\angle \mathrm{BAD}=45^{\circ}$. If $\mathrm{DC}=5 \mathrm{~cm}, \mathrm{BC}=4 \mathrm{~cm}$, the area of the trapezium in sq cm is

The points $(2, 1)$ and $(-3, -4)$ are opposite vertices of a parallelogram. If the other two vertices lie on the line $x + 9y + c = 0$, then $c$ is

A circle is inscribed in a rhombus with diagonals $12$ cm and $16$ cm. The ratio of the area of circle to the area of rhombus is

The area of a rectangle and the square of its perimeter are in the ratio $1:25$. Then the lengths of the shorter and longer sides of the rectangle are in the ratio

A parallelogram $ABCD$ has area $48 \mathrm{sqcm}$. If the length of CD is $8 \mathrm{~cm}$ and that of $AD$ is s cm , then which one of the following is necessarily true?

Points $E, F, G, H$ lie on the sides $A B, B C, C D$, and $D A$, respectively, of a square $A B C D$. If $E F G H$ 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

In a parallelogram $ABCD$ of area $72 \mathrm{sq} \mathrm{cm}$, the sides $CD$ and $AD$ have lengths $9 \mathrm{~cm}$ and $16 \mathrm{~cm}$, respectively. Let P be a point on $C D$ such that $A P$ is perpendicular to $C D$. Then the area, in sq cm, of triangle $A P D$ 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

If three sides of a rectangular park have a total length $400 \mathrm{ft}$, then the area of the park is maximum when the length (in ft ) of its longer side is