DEFINITION Triangle is a closed figure bounded by three straight lines called sides. It can also be defined as polygon of three sides. Area of triangle The area of the triangle is given by the following formulas: Given the base and the altitude See also the links below: CENTRES OF THE TRIANGLEDERIVATION OF HERON'S FORMULA
Derivation of Heron’s Formula for Area of Triangle
For a triangle of given three sides, say a, b, and c, the formula for the area is given by Derivation of Heron's Formula
Derivation of Formula for Radius of Incircle
The radius of in-circle is given by the formula DERIVATION
Derivation of Formula for Radius of Circumcircle
The formula for the radius of the circle circumscribed about a triangle (circumcircle) is given by
Derivation of Formula for Area of Cyclic Quadrilateral
For a cyclic quadrilateral with given sides a, b, c, and d, the formula for the area is given by DERIVATION OF THE FORMULA
Relationship Between Arithmetic Mean, Harmonic Mean, and Geometric Mean of Two Numbers
For two numbers x and y, let x, a, y be a sequence of three numbers. If x, a, y is an arithmetic progression then 'a' is called arithmetic mean. If x, a, y is a geometric progression then 'a' is called geometric mean. If x, a, y form a harmonic progression then 'a' is called harmonic mean. … Continue reading Relationship Between Arithmetic Mean, Harmonic Mean, and Geometric Mean of Two Numbers
Derivation of General term, Sum of Finite and Infinite Geometric Progression
Geometric Progression, GP Geometric progression (also known as geometric sequence) is a sequence of numbers where the ratio of any two adjacent terms is constant. The constant ratio is called the common ratio, r of geometric progression. Each term therefore in geometric progression is found by multiplying the previous one by r. Eaxamples of GP: 3, … Continue reading Derivation of General term, Sum of Finite and Infinite Geometric Progression
ARITHMETIC PROGRESSION – FORMULAS
Arithmetic Progression definition Arithmetic Progression (also called arithmetic sequence), is a sequence of numbers such that the difference between any two consecutive terms is constant. Each term therefore in an arithmetic progression will increase or decrease at a constant value called the common difference, d. Examples of arithmetic progression are: 2, 5, 8, 11,... common difference … Continue reading ARITHMETIC PROGRESSION – FORMULAS