Class 9 Maths — Chapter 10: HERON'S FORMULA

What you'll learn

• ▸Heron's Formula and Semi-Perimeter
• ▸Calculating Area from Three Known Sides
• ▸Finding Area with Perimeter and Two Sides
• ▸Finding Area with Side Ratios and Perimeter
• ▸Application to Special Triangles
• ▸Real-World Applications of Heron's Formula

Chapter Summary

--- PAGE 1 --- CHAPTER 10 HERON'S FORMULA 10.1 Area of a Triangle — by Heron's Formula We know that the area of triangle when its height is given, is ½ × base × height. Now suppose that we know the lengths of the sides of a scalene triangle and not the height. Can you still find its area? For instance, you have a triangular park whose sides are 40 m, 32 m, and 24 m. How will you calculate its area? Definitely 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. Try doing so. If you are not able to get it, then go to the next section. 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, triangl…

Practice Questions from this Chapter

Tap "Get Solution" on any question to ask our AI tutor.

1. Calculate triangle area using sides? Get Solution →
2. Show practical uses of Heron's Formula? Get Solution →
3. Solve complex triangle area problems? Get Solution →
4. What is the formula for the area of a triangle according to Heron's Formula? Get Solution →
5. In Heron's formula, what does the variable 's' represent? Get Solution →
6. How is the semi-perimeter 's' of a triangle with sides a, b, and c calculated? Get Solution →
7. The famous formula for the area of a triangle in terms of its three sides is named after whom? Get Solution →
8. When is Heron's formula particularly helpful for finding the area of a triangle? Get Solution →

Did you know?

• 💡 Heron of Alexandria invented the world's first steam engine, the aeolipile.
• 💡 Ancient Egyptians surveyed land using knotted ropes to create perfect right angles.
• 💡 The strongest geometric shape is the triangle because its structure resists deformation.
• 💡 Bees build their honeycombs using hexagons, which are tessellations of equilateral triangles.
• 💡 All pyramids, from ancient Egypt to Mexico, have triangular faces.

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