Quadrilateral
A quadrilateral is plane figure bounded by four straight lines. The straight line joining the opposite corners is called its… Click here to read more
Geometry
The Area of a Square
A square is a quadrilateral whose four angles are all right angles and whose all sides are equal. Let $$ABCD$$… Click here to read more
The Area of a Rectangle
A rectangle is a quadrilateral in which all four angles are right angles and the opposite sides are equal in… Click here to read more
The Area of a Parallelogram
A parallelogram is a quadrilateral whose opposite sides are of equal length and parallel. The diagonals of a parallelogram are… Click here to read more
The Area of a Rhombus
A rhombus is a quadrilateral having all sides with unequal diagonals which bisect each other. Note: If a square is… Click here to read more
The Area of a Trapezoid
A trapezoid is a quadrilateral with two sides parallel and the other two unparallel. The parallel sides of a trapezoid… Click here to read more
The Area of a Cyclic Quadrilateral
A quadrilateral inscribed is a circle is known as a cyclic quadrilateral. The proof is beyond the scope of this… Click here to read more
The Area of any Irregular Quadrilateral
A plane figure bounded by four straight line segments is called an irregular quadrilateral. The area of any irregular quadrilateral… Click here to read more
Regular Polygon
Introduction It is often necessary to determine the dimensions of a regular polygon inscribed in or circumscribed about a given… Click here to read more
Circumscribed and Inscribed Circle
Circumscribed Circle If a polygon is drawn in a circle so that every corner of the polygon lies on the… Click here to read more
Properties of a Regular Polygon
These are the properties of a regular polygon: The sides and interior angles of a regular polygon are all equal…. Click here to read more
Area of a Regular Polygon 1
Let $$AB = a$$ be the length of a side of a regular polygon of $$n$$ sides and $$O$$ be… Click here to read more
Area of a Regular Polygon 2
Area of a regular polygon of n sides when the radius r of the inscribed circle is given Since $$\angle… Click here to read more
Area of a Regular Polygon 3
Area of a regular polygon of n sides when the radius r of the circumscribed circle is given Let… Click here to read more
Introduction to Prisms
A prism is a solid whose ends, or bases, are parallel congruent polygons, and whose sides or faces are parallelograms…. Click here to read more
Lateral Surface Area of a Prism
The lateral surface area of a prism is the total of the area of the faces. $$\therefore $$Lateral Surface Area… Click here to read more
Volume of a Prism
Consider the right prism as shown in the figure below. There are as many cubic units in each layer parallel… Click here to read more
Prism Types
Cube The cube is a right prism with a square base and a height which is same as the side… Click here to read more
Introduction to Pyramids
A pyramid is solid figure whose base is a polygon and whose sides meet at a common point. This common point is… Click here to read more
Surface Area of a Pyramid
The surface area of a pyramid consists of the lateral surface, which is the area of the number of triangles… Click here to read more
Volume of a Pyramid
The cube shown in the figure illustrates the calculation of the volume of a pyramid. The opposite vertices of the cube… Click here to read more
Introduction to the Cone
A cone is a solid figure generated by a line, one end of which is fixed and the other end… Click here to read more
Volume of a Cone
The volume of a right circular cone is one-third of the volume of a right circular cylinder of the same… Click here to read more
Curved Surface Area of a Cone
If a perpendicular cut is made from a point on the circumference of the base to the vertex and the… Click here to read more
Introduction to Cylinders
Introduction Some curved surfaces may be defined as generated by straight lines which are thought of as moving and changing… Click here to read more
Right Circular Cylinder
Right Circular Cylinder A cylinder whose base is a circle is called circular cylinder. If the axis of the cylinder… Click here to read more
Hollow Circular Cylinder
Some examples of a hollow cylinder are pipes, circular buildings and bearing bushes. If $$R$$ is the outside radius of the cylinder… Click here to read more
Surface Area of Cylinders
(1) Right Circular Cylinder Curved surface area = the perimeter x the height of the cylinder, i.e. $$S = 2\pi rh$$ The… Click here to read more
Introduction to the Sphere
A sphere is a solid figure bounded by a curved surface, where every point of which is equidistant from a… Click here to read more
Surface Area of a Sphere
If we cover half of the surface of a sphere with a cord as shown in the figure, and then wind… Click here to read more
Volume of a Sphere
If a sphere is placed in a cylinder of the same diameter and with an height equal to the diameter and… Click here to read more
Spherical Shell
A solid enclosed between two concentric spheres is called a spherical shell. For a spherical shell, if $$R$$ and $$r$$… Click here to read more
Frustum of a Prism
Frustum When a plane section is taken of a right prism parallel to its end (i.e., perpendicular to its axis),… Click here to read more
Frustum of a Right Circular Cylinder
If $$r$$ is the radius and $$h$$ is the height of the frustum, then: (i) The volume of the frustum… Click here to read more
Frustum of a Pyramid
If a pyramid is cut through by a plane parallel to its base, the portion of the pyramid between that… Click here to read more
Frustum of a Cone
If a cone is cut by a plane parallel to its base, the portion of a solid between this plane… Click here to read more
Zone or Frustum of a Sphere
The portion of a sphere intercepted between two parallel planes is called a zone (i.e. a frustum). (i) The volume… Click here to read more
Introduction to Irregular Figures
A figure which is not uniform and regular in shape is an irregular figure. There are several practical situations where… Click here to read more
Trapezoidal Rule
To find the area of the trapezium as shown in the figure, the base $$AD$$ is divided into equal intervals… Click here to read more
Simpson’s Rule
The most important rule in practice is Simpson’s Rule because of its simplicity and accuracy. When more accuracy is required,… Click here to read more
The Circle and Parts of a Circle
The Circle A circle is a plane curve consisting of all points that have the same distance from a fixed… Click here to read more
Properties of the Circle
In geometry, a large number of facts about circles and their relations to straight lines, angles and polygons can be… Click here to read more
Area of a Circle
Consider the first figure and suppose that one semi-circle is cut from the center near the circumference in each direction. Then… Click here to read more
Relation Between the Circumference and Diameter
It we measure the circumference and diameter of various circles, we will find that the ratio of the circumference and… Click here to read more
Area of a Circular Ring or Annulus
Annulus: A circular ring (annulus) is plane figure bounded by the circumference of two concentric circles of two different radii…. Click here to read more
Area of a Sector
A sector is a portion of a circle bounded by two radii and the arc joining their extremities. It is… Click here to read more
Area of a Segment
A segment is a portion of a circle which is cut off by a straight line not passing through the… Click here to read more
Area of an Ellipse
Ellipse An ellipse is a curved line such that the sum of the distance of any point in it from… Click here to read more
Perimeter of an Ellipse
The perimeter or circumference of an ellipse is difficult to determine accurately. Various approximation formulas are given for finding the… Click here to read more
Introduction to Analytic Geometry
Geometry is one of the most ancient branches of mathematics, concerned with the properties of space and object – points,… Click here to read more