Heron’s formula Class 9 notes provided here will be a handy tool for students as it will help them understand the concept clearly and gain insight into the important questions given in the chapter. With these notes, students can further increase the possibility of scoring higher marks in the exams. Chapter 12 Heron’s Formula deals with topics, such as;
- Finding the area of a triangle using Heron’s formula
- Finding the area of quadrilaterals using Heron’s formula and other applications
In our previous classes, we have learned to find the area of the triangles using a simple formula, that is;
A = 1/2 x base x height
where the base and height of the triangle is known to us.
But in Heron’s formula, we will use the length of all the three sides of the triangle to calculate its area. Now let us see how it is possible.
Heron’s Formula For Class 9
Heron’s formula also referred to as Hero’s formula is named in honor of Hero of Alexandria who was a popular Greek mathematician in the early 10 – 70 AD century. This formula is used to find out the area of a triangle when the length of three sides a, b, c, are given or known. What’s different about this formula is that there is no need to find other distances in a triangle early on in comparison to what the other formulas state. Heron’s formula is quite useful in cases where it is not possible to find the height of the triangle easily.
The formula given by Heron about the area of a triangle is stated as;
Here, a, b and c are the three sides of the triangle.
Examples Of Heron’s Formula
Let us solve some problems based on Heron.s formula to understand the concept easily. Also, practice more questions with us.
Application of Heron’s Formula in Finding Areas of Quadrilaterals
Sometimes in farming lands, the shape of the fields are in quadrilaterals. In such cases, the quadrilateral area can be divided into triangular parts and then the formula for the area of the triangle can be used to calculate the sum. Suppose that a farmer has land to be cultivated and she employs some labourers for this purpose on the terms of wages calculated by area cultivated per square metre. How will she do this? Many a time, the fields are in the shape of quadrilaterals. We need to divide the quadrilateral into triangular parts and then use the formula for the area of the triangle. Let us look at this problem to understand it better:
- A park, in the shape of a quadrilateral ABCD, has ∠ C = 90º, AB = 10 m, BC = 11 m, CD = 4 m and AD = 9 m. How much area does it occupy?
- Find the area of a quadrilateral ABCD in which AB = 4 cm, BC = 5 cm, CD = 5 cm, DA = 6 cm and AC = 6 cm.
- A rhombus-shaped field has green grass for 20 cows to graze. If each side of the rhombus is 20 m and its longer diagonal is 45 m, how much area of grass field will each cow be getting?
- A triangle and a parallelogram have same base and same area. If the sides of the triangle are 20 cm, 25 cm and 35 cm, and the parallelogram stands on the base 30 cm, find the height of the parallelogram.
- An umbrella is made by stitching 12 triangular pieces of cloth of two different colours, each piece measuring 15 cm, 55 cm and 60 cm. How much cloth of each colour is required for the umbrella?
We at Byju’s are providing Heron’s formula for class 9 notes to helps students master concepts easily as well as study effectively.