Practice Problems on Heron’s Formula

Question 1. Find the area of a quadrilateral with side lengths of 6 cm, 8 cm, 10 cm, and 12 cm using Heron’s Formula (considering it as two triangles).

Question 2. A triangle has sides of lengths 3x, 4x, and 5x. Find the area of the triangle using Heron’s Formula in terms of x.

Question 3. Calculate the area of a triangle with sides of lengths 13 cm, 14 cm, and 15 cm using Heron’s Formula.

Question 4. An equilateral triangle has an area of 25√3 square units. Find the length of one of its sides using Heron’s Formula.

Question 5. If the sides of a triangle measure 17 cm, 25 cm, and 28 cm, what is its area using Heron’s Formula?

Heron’s formula is also known as Hero’s formula. It calculates the area of triangles or quadrilaterals based on the lengths of their sides. It does not consider the angles of the shapes, only their side lengths. The formula includes the semi-perimeter, which is symbolized by “s”, which is half the perimeter of the shape. This concept can be extended to find the area of quadrilaterals too.

Heron’s Formula for Area of Triangle

As we know Heron’s formula is used to calculate the area of a triangle,

Therefore, Heron’s Formula is

Area of Triangle ABC = √s(s-a)(s-b)(s-c)

where,

• s = Perimeter/2 = (a + b + c)/2

Area of Triangle Formulas

Formula to calculate different types of triangles is different. In the table given below, we have summarized the formulas for all the Types of Triangles.