Geometry Questions

The circumference of a circle exceeds its diameter by 30 cm. The area (in cm
2
) of the circle is: (Take π=
7
22
​
)

In a parallelogram, one of the parallel sides is $16\text{cm}$ and the other side is $12\text{cm}$. If the perpendicular distance between the two parallel sides of dimension $16\text{cm}$ is $24\text{cm}$, then the perpendicular distance between its other two parallel sides is:

In a rhombus, one diagonal is $40\text{cm}$ and the other diagonal is $22\text{cm}$ longer than half the first diagonal. Find the length of each side of the rhombus.

How many quadrilaterals are there in the given figure?

Starting from a point, Karan moves $6\text{km}$ in one direction and then $8\text{km}$ at a right angle to his initial path. What is the direct distance between his starting point and his final position?

A question along with a set of statements is given. Find which of the given statements is/are sufficient to answer the question.
Question: Find the perimeter of a triangle given that:
Statements:
I. Area of the triangle is $24\text{sq. units}$.
II. Height of the triangle is $4\text{units}$.

Atul walks 5 km toward North and then turns to the right. After walking 3 km he turns to the right and walks 5 km. How far away is he from his starting position?

Count the total number of squares in a standard $4\times 4$ grid matrix configuration:

The length and breadth of a rectangle are $12\text{cm}$ and $5\text{cm}$ respectively. What must be the length of its diagonal (in $\text{cm}$)?

Choose the figure which is different from the rest based on its boundary properties:

In ΔABC, D and E are points on sides AB and BC, respectively, such that DE∥AC. If BD=4 cm and AB=12 cm, then the ratio of the area of ΔBDE to that of quadrilateral ACED is:

In ΔABC, AB and AC are produced to points D and E, respectively. If the bisectors of ∠CBD and ∠BCE meet at point O such that ∠BOC=76
∘
, then ∠A= ?

Find out the number of triangles in the given figure.

When a cone is sliced by a plane parallel to its base, but not passing through its apex, what is the shape of the resulting cross-section?

Let A,B,C be the mid-points of sides XY,YZ and XZ, respectively of ΔXYZ. If the area of ΔXYZ is 8464 cm
2
, then find the area (in cm
2
) of ΔABC.

In ΔABC, P and Q are the middle points of the sides AB and AC, respectively. R is a point on the segment PQ such that PR:RQ=1:4. If PR=5 cm, then BC= ?

In $\Delta ABC$, $BD\perp AC$ at $D$. $E$ is a point on $BC$ such that $\angle BEA=x^{\circ }$. If $\angle EAC=36^{\circ }$ and $\angle EBD=40^{\circ }$, then the value of $x$ is:

In $\Delta ABC$, $AD$ is the bisector of $\angle A$ and intersects $BC$ at $D$. If $BC=a$, $AC=b$ and $AB=c$, then $BD$ is equal to:

Find the related word.
$$\pi :\text{Circle}::\varphi :?$$

In ΔXYZ, R and S are points on the sides XY and XZ respectively, such that RS is parallel to YZ. XR=15cm, XY=25cm, XS=12cm and XZ=20cm. RS is equal to:

If the volume of a cube is given as 12167cm
3
, then the surface area of the cube will be:

In ΔABC, D and F are the midpoints of the sides AB and AC, respectively. E is a point on the segment DF such that DE:EF=1:2. If DE=4cm, then BC is equal to:

If each edge of a cube is doubled, then the percentage increase in its total surface area is

If the distance between center to chord is $12\text{ cm}$ and the length of the chord is $10\text{ cm}$, then the diameter of the circle is

The diagonals $AC$ and $BD$ of a parallelogram $ABCD$ intersect each other at the point $O$. If $\angle DAC=32^{\circ }$ and $\angle AOB=70^{\circ }$, then $\angle DBC$ is equal to

In the following figure, $PAB$ is a secant and $PT$ is a tangent to the circle. If $PT=5\text{ cm}$ and $PA=3\text{ cm}$, then find the measurement of $AB$.

In the given figure $AB=AC$ and $\angle ACD=105^{\circ }$, then $\angle BAC$ is equal to

In the given figure, ABCD is a cyclic quadrilateral. Then the ordered pair (x, y) is

The perimeter of a rhombus whose diagonals are $10\text{cm}$ and $24\text{cm}$ is

In a cyclic quadrilateral ABCD, the opposite interior angles are given as linear expressions: ∠A=(4y+20)
∘
, ∠B=(3y−5)
∘
, ∠C=(4x)
∘
, and ∠D=(7x+5)
∘
. Find the values of the ordered pair (x,y).

The perimeter of a rhombus whose diagonals are 10cm and 24cm is

In the diagram, the lines QR and ST are parallel to each other. The shortest distance between these two lines is half the shortest distance between the point P and line QR. What is the ratio of the area of the triangle PQR to the area of the trapezium SQRT?(Note: Assume the text asks for the ratio of Area of PQR to Area of SQRT based on the mathematical constraints provided)

In which of the following molecules, all atoms are coplanar?

${\text{XeF}}_2$ is isostructural with: