Area of Triangle

The area of a triangle is defined as the total space that is enclosed by any particular triangle. The basic formula to find the area of a given triangle is A = 1/2 × b × h, where b is the base and h is the height of the given triangle, whether it is scalene, isosceles or equilateral.

Examples:

  • To find the area of the triangle with base b as 3 cm and height h as 4 cm, we will use the formula for
  • Area of a Triangle – A = 1/2 × b × h = 1/2 × 4 cm × 3 cm = 2 cm × 3 cm = 6 cm2

Table of Content

In general, the term “area of a triangle” is defined as the region occupied inside the boundary of a flat object or figure. The measurement is done in square units with the standard unit being square meters (m2). For the computation of area, there are pre-defined formulas for squares, rectangles, circle, triangles, etc.

In this article, we will learn the area of triangle formulas for different types of triangles, along with some example problems.

Area of Triangle

Area of a Triangle Formula

The area of the triangle  is given by the formula mentioned below:

  • Area of a Triangle = A = ½ (b × h) square units, where a, b, and c are the three sides of a triangle.

Now, let’s see how to calculate the area of a triangle using the given formulas. The area formulas for all the different types of triangles like an area of an equilateral triangle, right-angled triangle, an isosceles triangle are given below.

Area of a Right Angled Triangle

A right-angled triangle or also called a right triangle have one angle at 90° and the other two acute angles sums to 90°. Therefore, the height of the triangles will be the length of the perpendicular side.

Area of a right angled triangle

  • Area of a Right Triangle = A = ½ × Base × Height(Perpendicular distance)

Area of an Equilateral Triangle

An equilateral triangle has all its sides as equal. The perpendicular drawn from the vertex of the triangle to the base divides the base into two equal parts. To calculate the area of the equilateral triangle, we have to know the measurement of its sides.

Area of a equilateral triangle

  • Area of an Equilateral Triangle = A = (√3)/4 × side2

Area of an Isosceles Triangle

An isosceles triangle has two of its sides equal and also the angle opposite the equal sides are equal.

area of a isosceles triangle

  • Area of an Isosceles Triangle = A = ½ (base × height)

Perimeter of a Triangle

The perimeter of a triangle is the distance covered around the triangle and is calculated as the sum of all the three sides of it.

  • The perimeter of a triangle = P = a + b + c units

Area of Triangle with Three Sides-By Heron’s Formula

The area of a triangle with three sides can be found using Heron’s formula if all the three sides of the triangle are given. Heron’s formula needs the measurement of all three sides of the triangle as it is used to find the semi perimeter first and then using the same in the main formula to find the area of the triangle.

Area of triangles for three sides-Heron's formulawhere, s is semi-perimeter of the triangle = (a+b+c) / 2

We have seen that the area of special triangles could be obtained using the triangle formula. However, for a triangle with the sides being given usually, calculation of height would not be simple. For the same reason, we rely on Heron’s Formula to calculate the area of the triangles with unequal lengths.

Solved Examples

Example 1: Find the area of an acute triangle with a base of 13 inches and a height of 5 inches.

Solution:

A = (½)× b × h sq.units

⇒ A = (½) × (13 in) × (5 in)

⇒ A = (½) × (65 in2)

⇒ A = 32.5 in2

Example 2: Find the area of a right-angled triangle with a base of 7cm and a height of 8cm.

Solution:

A = (½) × b × h sq.units

⇒ A = (½) × (7 cm) × (8 cm)

⇒ A = (½) × (56 cm2)

⇒ A = 28 cm2

Example 3: Find the area of an obtuse-angled triangle with a base of 4cm and a height 7cm.

Solution:

A = (½) × b × h sq.units

⇒ A = (½) × (4 cm) × (7 cm)

⇒ A = (½) × (28 cm2)

⇒ A = 14 cm2

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Frequently Asked Questions

How to find the area of a triangle given three sides?

When the values of the three sides of the triangle are given, then we can find the area of that triangle by using Heron’s Formula. Refer to the section ‘Area of a triangle by Heron’s formula‘ mentioned in this article for complete brief.

How to find the area of a triangle using vectors?

Suppose vectors u and v are forming a triangle in space. Then, the area of this triangle is equal to half of the magnitude of the product of these two vectors, such that,

 A = ½ |u + v|

How to calculate area of triangle?

For a given triangle, where base of the triangle is b and height is h, the area of the triangle can be calculated by the formula, such as;

A = ½ (b × h) Square Unit


To learn more about the computation of the area of a triangle using Heron’s Formula, keep visiting BYJU’S – The Learning App.

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