Area of Triangle
The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h. This formula is applicable to all types of triangles, whether it is a scalene triangle, an isosceles triangle, or an equilateral triangle. It should be remembered that the base and the height of a triangle are perpendicular to each other.
In this lesson, we will learn the area of triangle formulas for different types of triangles, along with some examples.
What is the Area of a Triangle?
The area of a triangle is the region enclosed within the sides of the triangle. The area of a triangle varies from one triangle to another depending on the length of the sides and the internal angles. The area of a triangle is expressed in square units, like, m2, cm2, in2, and so on.
Triangle Definition
A triangle is a closed figure with 3 angles, 3 sides, and 3 vertices. It is one of the most basic shapes in geometry and is denoted by the symbol △. There are different types of triangles in math that are classified on the basis of their sides and angles.
Area of Triangle Formula
The area of a triangle can be calculated using various formulas. For example, Heron’s formula is used to calculate the triangle’s area, when we know the length of all three sides. Trigonometric functions are also used to find the area of a triangle when we know two sides and the angle formed between them. However, the basic formula that is used to find the area of a triangle is:
Area of triangle = 1/2 × base × height
Observe the following figure to see the base and height of a triangle.
Let us find the area of a triangle using this formula.
Example: What is the area of a triangle with base 'b' = 2 cm and height 'h' = 4 cm?
Solution: Using the formula: Area of a Triangle, A = 1/2 × b × h = 1/2 × 4 × 2 = 4 cm2
Triangles can be classified based on their angles as acute, obtuse, or right triangles. They can be scalene, isosceles, or equilateral triangles when classified based on their sides. Let us learn about the other ways that are used to find the area of triangles with different scenarios and parameters.
