Examples on Area of Triangle with 3 Sides

Example 1: Find the area of a triangle with measure of three sides as 3 cm, 4 cm and 5 cm respectively.

Solution:

We know that,

Area of triangle, A = √{s(s-a)(s-b)(s-c)} , and

Semi-Perimeter, s = (a+b+c)/2

⇒ s = (3+4+5)/2 = 6 cm

Now Area of triangle, A = √{6(6-3)(6-4)(6-5)} = √(6x3x2x1) = 6 cm²

Thus, area of triangle with three sides as 3 cm, 4 cm and 5 cm respectively is found to be 6 cm² using Heron’s Formula.

Example 2: A triangle has its three sides as 6 cm, 8 cm and 10 cm, Find its area.

Solution:

Here, a = 6 cm, b = 8 cm, and c = 10 cm

We know that,

Area of triangle, A = √{s(s-a)(s-b)(s-c)}

where, s = (a+b+c)/2 = (6+8+10)/2 = 12

⇒ A = √{12x(12-6)x(12-8)x(12-10)}

⇒ A = √(12x6x4x2) = 24 cm²

⇒ A = 24 cm²

Example 3: Derive an expression for area of an equilateral triangle with each having side length = a.

Solution:

According to Heron’s formula, we have, A = √{s(s-a)(s-b)(s-c)}

For equilateral triangle, a = b = c

⇒ A = √{s(s-a)(s-a)(s-a)} = √{s(s-a)³}

Putting, s = (a+a+a)/2 = 3a/2, we get,

⇒ A = √{3a/2(3a/2-a)³}

⇒ A = √3a²/4

Area of Triangle when measures of its three sides are given is found using Heron’s formula. The area of any two-dimensional shape is the measure of a region’s size on a surface. A triangle is a closed polygon having three sides and three vertices. Area of a triangle can be found using different methods. One of them includes determining the area using measures of the length of each side of the triangle.

In this article, we will discuss that method, the formula, and some solved examples based on the calculation of the area of a triangle with three sides.