Geometry Questions

Select the correct statement about the properties of a triangle.

Which of the following is NOT a criterion of congruent triangles?

The internal angle bisectors BI and CI of ∠B and ∠C of a ΔABC meet at point I. If ∠A=38
∘
, then what is ∠BIC equal to?

The longest chord of a circle is equal to:

△XYZ is an isosceles triangle such that XY=XZ. It is given that YS⊥XZ and ZT⊥XY. What is the relation between YS and ZT?

A clock shows the time as $7:15$. What is the angle between the hour and the minute hand?

How many squares can you count in the given figure?

The difference between the total surface area and lateral surface area of a cube, if side of the cube is 11cm (in square cm), is ___________.

The lengths of the three sides of a triangle are given as 3cm, 4cm and 5cm. The ratio of their corresponding altitudes to the opposite vertices will be:

A 70cm wide path is made around a circular garden having a diameter of 14 metres. What is the area of the path (in m
2
)?

A hollow copper pipe is 22cm long and its external diameter is 28cm. If the thickness of the pipe is 3cm and iron weighs 8.5g/cm
3
, then the weight of the pipe is closest to:

The slant height of a right circular cone is 15m and its height is 9m. The area of its curved surface is:

A right triangle with sides 5cm,12cm and 13cm is rotated about the side 12cm to form a cone. The volume of the cone so formed is:

Find the number of triangles in the figure.

Find the number of triangles in the figure.

Find the number of triangles in the figure.

If you have a regular icosahedron and you slice it along a plane that intersects six of its faces, what is the shape of the resulting cross-section?

Calculate the area of a rectangle whose length is $17.2\text{cm}$ and width is $13.4\text{cm}$.

The length of cold storage of cuboidal shape is double its breadth and its height is half of its breadth. If its volume is 216m
3
, then what are the dimensions of the cold storage?

The diagonal of a cubical block of wood is
192

​
cm. Find its volume.

Which of the following statements is correct?The angle between two tangents to a circle may be $0^{\circ }$.If a transversal intersects two lines such that a pair of alternate interior angles is equal, then the two lines are parallel.The tangents at the end points of a diameter of a circle are perpendicular.

If $M$ is the mid-point of the side $BC$ of $\Delta ABC$, and the area of $\Delta ABM$ is $19{\text{cm}}^2$, then the area of $\Delta ABC$ is:

The lateral surface area of a cylinder is 3862.2cm
2
and its height is 15cm. Find its volume (take π=3.14) correct to one decimal place.

A rhombus has a perimeter of $122.2\text{metres}$. Find the length of each side of the rhombus.

A circle and a rectangle have the same perimeter. If the sides of the rectangle are 15cm and 7cm, then the area of circle is:

If V and S denote the volume and Total Surface Area of a cuboid (of sides a,b,c), respectively, then which of the following is true?

Find out the related word to complete the analogy.
$$\text{Triangle : Polygon :: Square : ?}$$

What is the shape of the cross-section, when a cone is cut by a plane parallel to its slant height?

In $\Delta PQR$, $S$ and $T$ are points on the sides $PQ$ and $PR$, respectively, such that $\Delta PST$ is similar to $\Delta PRQ$. If $\text{m}\angle PQR=47^{\circ }$, then find $\text{m}\angle STR$.

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:

If the length of each of the two equal sides of an isosceles triangle is 15 cm and the adjacent angle is 30°, then the area of the triangle is:

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

If you have a regular pentagonal prism and you slice it parallel to its bases, what shape is the cross-section?

The perimeter of an isosceles right-angled triangle having an area of 200cm
2
is:

What is the area (in cm
2
) of a sector of a circle, with central angle 75
∘
, when the diameter of the circle is 9cm?

Count the number of triangles in the given figure.

Determine the number of pentagons in the following figure.

Two triangles $PRS$ and $DEF$ are similar whose perimeters are $36\text{cm}$ and $40\text{cm}$, respectively. If the length of $DE$ is $10\text{cm}$, then what is the length (in $\text{cm}$) of $PR$?

The area of a triangle whose sides are $3\text{cm}$, $5\text{cm}$, and $6\text{cm}$ is:

In △ABC, AB=9cm and AC=13cm, then the length of BC could be:

What is the perpendicular distance (in cm) between the parallel sides of a trapezium whose area is 108sq cm and the lengths of the parallel sides are 9cm and 36cm?

If x
2
−1, 2x and x
2
+1 are the three sides of a right-angled triangle, then which of the following can be its hypotenuse?

The median AD of a triangle ABC is produced and a perpendicular CF is dropped on it. BE is perpendicular to AD. If BC=34cm and DF=8cm, what is the length (in cm) of BE?

Find the area (in cm
2
) of a circle with a maximum radius that can be inscribed in a rectangle of length 18cm and breadth 12cm.

PQ is a diameter of a circle and PS is a chord. If PQ is 82cm and PS is 80cm, the distance (in cm) of PS from the center of the circle is:

How many rectangles are there in the given figure?

What is the area of a triangle with base $8\text{meters}$ and height $16\text{meters}$?

In △ABC and △PQR, AB=7m, BC=8m, AC=9m, PQ=7m, QR=8m and PR=9m. Which of the following is true for these triangles?

If the angles of a triangle are in the ratio of 9:11:16, then the difference between the greatest angle and the smallest angle is:

Find the area of a right angle whose base is 15 cm and hypotenuse is 17 cm.

Three solid iron cubes of edges 8 cm, 10 cm and 12 cm are melted together to make a new cube. It is observed that 496 cm³ of the melted material is lost due to improper handling. The area (in cm²) of the whole surface of the newly formed cube is:

If the surface areas of two spheres are in the ratio of 9: 49, then the ratio of their volumes is:

The ratio of length and breadth of a rectangle is $21:20$ and its perimeter is $164\text{cm}$. What is the length of its diagonal (in cm)?

The square of the diagonal of a cube is 2346 cm
2
. What is the total surface area (in cm
2
) of the cube?

In △ABC and △PQR, we are given ∠A=∠P and AC=PR.
Which of the following options needs to be satisfied for △PQR and △ABC to be congruent?