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Facts That Matter- Heron’s Formula | Mathematics (Maths) Class 9 PDF Download

Facts That Matter- Heron’s Formula | Mathematics (Maths) Class 9

  • Area of a triangleFacts That Matter- Heron’s Formula | Mathematics (Maths) Class 9
  • Heron’s formula: For sides of a triangle being a, b, c, the semi-perimeterFacts That Matter- Heron’s Formula | Mathematics (Maths) Class 9 and area of the triangle = Facts That Matter- Heron’s Formula | Mathematics (Maths) Class 9
  • For finding the area of a quadrilateral, we divide it into various triangles. Then we use Heron’s formula to find the area of the triangles.

Area of Triangle

We have already learnt that area of a triangle
Facts That Matter- Heron’s Formula | Mathematics (Maths) Class 9[altitude corresponding to that side (or height)]
Facts That Matter- Heron’s Formula | Mathematics (Maths) Class 9
Facts That Matter- Heron’s Formula | Mathematics (Maths) Class 9 [altitude corresponding to base (or height)]

Facts That Matter- Heron’s Formula | Mathematics (Maths) Class 9

Thus, the area of a triangleFacts That Matter- Heron’s Formula | Mathematics (Maths) Class 9

Note: 
Unit of measurement for area of any plane figure is taken as square metre (m2) or square centimetre (cm2), etc.

Heron's Formula

When it is not possible to find the height of the triangle easily and measures of all the three sides are known then we use Heron’s formula, which is given by
Area of a triangle =Facts That Matter- Heron’s Formula | Mathematics (Maths) Class 9
where a, b and c are the sides of the triangle and s = semi-perimeter, i.e. half the perimeter of the triangle =Facts That Matter- Heron’s Formula | Mathematics (Maths) Class 9

Area of an Equilateral Triangle

Let the side of the equilateral triangle be ‘a’.
Facts That Matter- Heron’s Formula | Mathematics (Maths) Class 9
⇒ Area of the triangle
Facts That Matter- Heron’s Formula | Mathematics (Maths) Class 9

Facts That Matter- Heron’s Formula | Mathematics (Maths) Class 9
Thus, the area of an equilateral triangleFacts That Matter- Heron’s Formula | Mathematics (Maths) Class 9

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FAQs on Facts That Matter- Heron’s Formula - Mathematics (Maths) Class 9

1. What is Heron's formula?
Ans. Heron's formula is a mathematical formula used to find the area of a triangle when the lengths of all three sides are known. It is named after Hero of Alexandria, who first derived this formula.
2. How is Heron's formula derived?
Ans. Heron's formula is derived using the semi-perimeter of a triangle. The semi-perimeter is calculated by adding the lengths of all three sides of the triangle and dividing the sum by 2. Then, using the semi-perimeter and the lengths of the three sides, the area of the triangle can be calculated using the formula √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter and a, b, and c are the lengths of the sides.
3. What is the significance of Heron's formula?
Ans. Heron's formula is significant because it provides a simple and efficient way to calculate the area of a triangle without needing the height or any angles. It is especially useful when the height of the triangle is not known or difficult to measure.
4. Can Heron's formula be used for all types of triangles?
Ans. Yes, Heron's formula can be used for all types of triangles, including equilateral, isosceles, and scalene triangles. As long as the lengths of all three sides are known, Heron's formula can be applied to find the area of the triangle.
5. What are some real-life applications of Heron's formula?
Ans. Heron's formula has various real-life applications, such as calculating the area of land with irregular shapes, determining the area of a field for farming, calculating the area of a triangular roof, or finding the area of a triangular garden bed. It is also used in geometry and trigonometry to solve various problems and equations related to triangles.
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