CAT Result 2024 - Expected Date, IIM CAT Scorecard & Percentile, How to Check Direct link @iimcat.ac.in

CAT Area of a Triangle — by Heron’s Formula - Practice Questions & MCQ

Edited By admin | Updated on Oct 04, 2023 04:20 PM | #CAT

Concepts Covered - 1

Area of a Triangle — by Heron’s Formula

Till now, we have studied that how to find area of right angle, equilateral, isosceles triangle. In these triamgles, height is given or can be found using Pythagoras Theorem.

Now suppose that we know the lengths of the sides of a scalene triangle and not the height. Can you still find its area? If you want to apply the formula, you will have to calculate its height. But we do not have a clue to calculate the height.

Let's see a formula, where we don't have to calculate height to find the area of any triangle.

Heron’s Formula

The formula given by Heron about the area of a triangle, is also known as Hero’s formula. It is stated as:

$\text{Area of a triangle }=\sqrt{s(s-a)(s-b)(s-c)}$ , where a, b and c are the sides of the triangle, and s = semi-perimeter, i.e., half the perimeter of the triangle = $\frac{a+b+c}{2}$ .

This formula is helpful where it is not possible to find the height of the triangle easily.

TIP:-

Heron was born in about 10AD possibly in Alexandria in Egypt. He worked in applied mathematics. His works on mathematical and physical subjects are so numerous and varied that he is considered to be an encyclopedic writer in these fields. His geometrical works deal largely with problems on mensuration written in three books. Book I deals with the area of squares, rectangles, triangles, trapezoids (trapezia), various other specialised quadrilaterals, the regular polygons, circles, surfaces of cylinders, cones, spheres etc. In this book, Heron has derived the famous formula for the area of a triangle in terms of its three sides.