Area of Triangle Formula: How to Calculate, Example with Solution

Area of Triangle Formula: In general, "area" refers to the region inside the boundary of a flat object or figure and is measured in square units, with the standard unit being square meters (m²). There are specific formulas to compute the area of different geometric shapes such as squares, rectangles, circles, and triangles. In this article, we explore the area of triangles and its formulas for various types of triangles, including some example problems to illustrate their application.The area of a triangle is a measurement of the space enclosed within its three sides in 2D. A triangle is a closed shape with three sides and three vertices. The general formula to calculate the area of a triangle is half of the product of its base and height. Let’s explore the topic in detail.

Triangle Definition and Types

A triangle is a closed, 2-dimensional polygon with 3 sides, 3 angles, and 3 vertices. 

Types of Triangle based on the length of sides

Equilateral triangle: all sides of triangle are equal

Isosceles triangle: two sides of triangle are equal

Scalene triangle: three sides of triangle are equal

Types of Triangle based on the angles 

Acute-angled Triangle: all interior angles are acute i.e less than 90 degree.

Right-angled Triangle: one of the three interior angle is 90 degree.

Obtuse-angled Triangle: one of the three interior angle more than 90 degree.

What is the Area of A Triangle?

The area of any triangle is the total region enclosed within the triangle's three sides. 

Area of Triangle Formula

Area of a triangle is half the product of its base and height.

Therefore, to calculate the area of a triangle, one should have its base and height measurements.

Area of Triangle = ½ * b* h sq units

Where, b = base and h = height.

Area of A Right Angled Triangle

Area of Triangle = ½ * b* h sq units

In the case of a right-angled triangle, 

Height (h) is the perpendicular distance between base (b) and top vertix.

Hence, Area of A Right Angled Triangle = ½ * b* h sq units

Area of An Equilateral Triangle

To calculate the area of an equilateral triangle, use the formula below:

Area of An Equilateral Triangle = (√3)/4 × side2

Area of An Isosceles Triangle

Area of an isosceles triangle = ¼ b√4a2-b2

Here, a, b are the sides of the isosceles triangle.

Heron’s Formula: Area of Scalene Triangle

Area of a triangle where all 3 sides have different measures, can be calculated using Heron’s formula.

Heron’s formula A = √s(s-a)(s-b)(s-c)

Here, semiperimeter of the triangle s = ½ (a+b+c)

a, b, c are sides of the triangle.

Solved Examples

Example 1: The base of a triangle is 12 cm and height 5 cm. Find out the area of a triangle.

Solution: 

Area of Triangle = ½ * b* h sq units

A = ½ * 12 * 5 

A = 30 cm2

Example 2: What is the area of an equilateral triangle with side 10cm.

Solution:

Area of an equilateral triangle = √3a2/4

= √3(8)2/4

= 16√3 cm2

Example 3: Use Heron’s formula to find the length of a triangle ABC which has sides 3cm, 4 cm and 5cm long.
Solution:
A = √(s(s-a)(s-b)(s-c))

Where s = (a+b+c)/2
Thus, s = (4+3+5)/2 cm
s = 6 cm
Substituting the values,
A = √(6(6-4)(6-3)(6-5)) cm2
⇒ A = √(6(2)(3)(1)) cm2
⇒ A = √(36) cm2 = 6 cm2
The area of the triangle is 6 cm2.