Q1
Heron's formula is used to find the:
Aarea of a triangle using its sides
Bperimeter of a triangle
Cangles of a triangle
Dvolume of a triangle
CBSEClass 9 (CBSE)MathematicsCh 10 · Topic 1
Understanding Heron's Formula
Learning to calculate the area of a triangle using its three sides.
Core concept
For example, for a triangle with sides 5, 6, 7, the semi-perimeter is s = (5+6+7)/2 = 9, and the area is √(9×(9-5)×(9-6)×(9-7)) = √(9×4×3×2) = √216 ≈ 14.7 square units. This formula, attributed to the ancient Greek mathematician Heron of Alexandria, works for any triangle (not just right triangles), making it a versatile tool whenever three side lengths are known but the height is not.
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• Heron's Formula: Area = √(s(s-a)(s-b)(s-c)), where s = (a+b+c)/2 (semi-perimeter).
• This formula uses only the three side lengths, no height needed.
• Example: sides 5,6,7 give semi-perimeter 9 and area √216 ≈ 14.7 sq units.
• Heron's Formula works for any triangle, not just right triangles.