Table of Contents
Formulas to Calculate the Area of Triangles
and Quadrilaterals
The area of a triangle can be calculated using the following formula:
A = base × height
The area of a quadrilateral can be calculated using the following formula:
A = base 1 + base 2 + base 3 + base 4
What is an Area?
An area is a measure of how much space is enclosed by a two-dimensional figure. The area is the product of the length and width of the figure.
What is a Triangle?
A triangle is a three-sided polygon. It has three vertices and three angles.
How to Find the Area of a Triangle?
The area of a triangle is equal to one-half the base multiplied by the height.
Heron’s Formula
In mathematics, Heron’s formula, also called Hero’s formula, is a geometric formula that gives the area of a triangle, in terms of its three sides. The formula states that the area is:
where a, b, and c are the lengths of the triangle’s sides, and s is its semiperimeter.
Heron’s formula can also be used to find the length of a side of a triangle, given the other two sides and the triangle’s area. This is done by solving for c in the equation
where a and b are the other two sides.
Calculation of Semi-Perimeter
Semi-perimeter of a triangle is the sum of the lengths of its sides divided by two.
Semi-perimeter = (length of Side 1 + length of Side 2 + length of Side 3) / 2
When any two sides of a Right-Angled Triangle are given
, the third side can be found.
The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the length of the long side.
When the side of the Equilateral Triangle is given
If the side of an equilateral triangle is given, the length of the triangle’s side can be found using the Pythagorean theorem. The equation for the Pythagorean theorem is a^2 + b^2 = c^2, where a, b, and c are the length of the triangle’s three sides.
When the Vertices of a Triangle on the Coordinate Plane are given
If the vertices of a triangle are given as points (x 1 , y 1 ), (x 2 , y 2 ), and (x 3 , y 3 ), then the equation of the triangle is:
y = x 1 2 + x 2 2 + x 3 2
For more visit How To Find The Area Of A Triangle Using Vectors?
