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Quantitative Aptitude – Geometry – Formula

1. What is Geometry ?

Geometry is a branch of mathematics that deals with shape, size, relative position of figures, and the properties of space. It emerges independently in number of early cultures as a practical way of dealing with lengths, area and volumes.

Geometry can be divided into two different types: Plane Geometry and Solid Geometry. The Plane Geometry deals with shapes such as circles, triangles, rectangles, square and more. Whereas, the Solid Geometry is concerned in calculating the length, perimeter, area and volume of various geometric figures and shapes. And are also used to calculate the arc length and radius
etc.

2. What is Angle ?

Angle is formed when two rays intersect i.e. half-lines projected with a common endpoint. The corner points of angle is known as the vertex of the angle and the rays as the sides, i.e. the lines are known as the arms. It is defined as the measure of turn between the two lines. The unit of angle is radians or degrees. There are different types of formulas for angles some of them are double-angle formula, half angle formula, compound angle formula, interior angle formula etc.

3. What is Area ?

Area is the size of a two-dimensional surface. It is defined as the amount of two-dimensional space occupied by an object. Area formulas have many practical applications in building, farming, architecture, science. The area of a shape can be determined by placing the shape over a grid and counting the number of squares that covers the entire space. For example, area of square can be calculated using a2 where, a is the length of its side.

4. What is Volume ?

The volume of an object is the amount of space occupied by the object, which is three dimensional in shape. It is usually measured in terms of cubic units.

5. What is Midpoint ?

Midpoint formula is used to find the center point of a straight line. Sometimes you will need to
find the number that is half of two particular numbers. For that, you find the average of the two
numbers. In that similar fashion, we use the midpoint formula in coordinate geometry to find the
halfway number (i.e. point) of two coordinates.

6. What is Vertex ?

In geometry, a vertex is a point where two or more curves, lines, or edges meet. As a consequence of this definition, the point where two lines meets to form an angle and the corners of polygons
and polyhedral are vertices.

7. What is Triangle ?

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in
geometry. A triangle with vertices A, B, and C. The length of the sides of a triangle may be same
or different. If all the 3 sides of a triangle are equal, then it is an equilateral triangle.

8. What is Rectangle ?

Rectangle formulas include the formula for area, perimeter, and diagonal of a rectangle. To recall,
a rectangle is a four sided polygon and the length of the opposite sides are equal. A rectangle is
also called as an equiangular quadrilateral, as all the angles of a rectangle are right angled. A
rectangle is a parallelogram with right angles in it. When the four sides of a rectangle are equal,
then it is called a square.

9. What is Circle ?

Circle is a particular shape and defined as the set of points in a plane placed at equal distance from a single point called the center of the circle. We use the circle formula to calculate the area,
diameter, and circumference of a circle. The length between any point on the circle and its center is known as its radius.

10. What is parabola ?

A set of points on a plain surface that forms a curve such that any point on the curve is at
equidistant from the focus is a parabola. One of the properties of parabolas is they are made of a
material that reflects light that travels parallel to the axis of symmetry of a parabola and strikes
its concave side which is reflected its focus. It divides the graph into two equal parts.

11. What is Cylinder?

The volume of a cylinder is the density of the cylinder which signifies the amount of material it
can carry or how much amount of any material can be immersed in it. It is given by the formula,
πr2h, where r is the radius of the circular base and h is the height of the cylinder.

12. What is Pyramid ?

A polyhedron that has a polygonal base and triangles for sides is a pyramid. The three main parts
of any pyramid’s: apex, face and base. The base of a pyramid may be of any shape. Faces usually
take the shape of an isosceles triangle. All the triangle meets at a point on the top of the pyramid
that is called “Apex”.

13. What is Sphere ?

A perfectly symmetrical 3 – Dimensional circular shaped object is a Sphere. The line that connects
from the center to the boundary is called radius of the square. You will find a point equidistant
from any point on the surface of a sphere. The longest straight line that passes through the center of the sphere is called the diameter of the sphere. It is twice the length of the radius of the sphere.

14. What is Axis of symmetry ?

Axis of symmetry is a line that divides an object into two equal halves, thereby creating a mirror
like reflection of either side of the object. The word symmetry implies balance. Symmetry can be
applied to various contexts and situations.

15. What is Hexagon ?

A polygon is a two-dimensional (2-D) closed figure made up of straight line segments. In geometry, hexagon is a polygon with 6 sides. If the lengths of all the sides and the measurement of all the angles are equal, such hexagon is called a regular hexagon. In other words, sides of a regular hexagon are congruent.

16. What is Polygon ?

Polygon is a word derived from The Greek language, where poly means many and gonna means
angle. So we can say that in a plane, closed figure with many angles is called a polygon.

17. What is Rotation ?

Think of a compass and draw a circle, the point where you put the pin to rotate the compass to
draw the circle, is the point which is called as a “centre of rotation”. The rotation turns the circle
through an angle. Rotation can be done clockwise as well as counter clockwise. The most common rotation angles are 90 degrees, 180 degrees, 270 degrees etc.

18. What is Cyclic quadrilateral ?

A quadrilateral whose vertices lie on a single circle is called cyclic quadrilateral. This circle is
called the circum circle, and the vertices are known to be con cyclic.

19. What is perimeter ?

A perimeter means the distance of the boundary of a two dimensional shape. Also defined as the
total sum of the length of all the sides of the object.

20. What is Surface area ?

Surface area formulas in geometry refer to the lateral surface and total surface areas of different
geometrical objects. To recall, the surface area of an object is the total area of the outside surfaces of the three-dimensional object i.e., the total sum of the area of the faces of the object.

21. What is Equation of a Line ?

An equation of a line can be expressed in many ways – Slope Intercept, Standard or Point-Slope.
Here we will discuss Point-Slope Equation of a Line.

22. What is Slope ?

The slope formula is used to calculate the steepness or the incline of a line. The x and y
coordinates of the lines are used to calculate the slope of the lines. It is the ratio of the change in
the y-axis to the change in the x-axis.

23. What is Tangent line ?

The line that touches the curve at a point called the point of tangency is a tangent line.

24. What is Square ?

Square is a regular quadrilateral. All the four sides and angles of a square are equal. The four
angles are 90 degrees each, that is, right angles.

25. What is Octagon ?

A polygon is a two-dimensional (2-D) closed figure made up of straight line segments. In
geometry, the octagon is a polygon with 8 sides. If the lengths of all the sides and the
measurement of all the angles are equal, the octagon is called a regular octagon.

26. What is Ellipse ?

In geometry, an ellipse is described as a curve on a plane that surrounds two focal points such
that the sum of the distances to the two focal points is constant for every point on the curve. In
the following figure, F1 and F2 are called the foci of the ellipse.

27. What is Hyperbola ?

In simple sense, hyperbola looks similar to mirrored parabolas. The two halves are called the
branches. When the plane intersects on the halves of a right circular cone angle of which will be
parallel to the axis of the cone, a parabola is formed. A hyperbola contains: two foci and two
vertices.

28. What is Cone ?

Cone is a three-dimensional structure having a circular base where a set of line segments,
connecting all of the points on the base to a common point called apex. There is a predefined set
of formulas for the calculation of curved surface area and total surface area of a cone which is
collectively called as cone formula.

29. What is prism ?

A polyhedron with two polygonal bases parallel to each other is a prism. In optics, the prism is
the transparent optical element with flat polished surfaces that refract light.

30. What is Rate of Change ?

The dictionary meaning of slope is a gradient, pitch or inclines. This formula is used to measure
the steepness of a straight line.

31. What is Parallelogram ?

A geometric shape with two similar opposite sides and equal opposite angles is a parallelogram.
This is termed a parallelogram when the image is two dimensional and if the image is three
dimensional, then it is termed as parallelepiped.

32. What is Great Circle ?

The largest circle that can be drawn on the sphere surface is the great circle. The shortest
distance between any two points on the sphere surface is the Great Circle distance.

33. What is The Distance ?

In analytic geometry, the distance between two points of the xy-plane can be found using the
distance formula. Distance Formula is used to calculate the distance between two points.

34. What is Tangential Quadrilateral ?

In geometry, the tangential quadrilateral is a convex quadrilateral whose sides are all tangent to a
single circle within the quadrilateral. This circle is called the in circle of the quadrilateral or its
inscribed circle, its center is the in center and its radius is called the in radius.

35. What is Asymptote ?

Asymptote is defined as a line which is tangent to a curve at infinity. There are two types of
asymptote: one is horizontal and other is vertical. Below mentioned is asymptote formula.