Heron's Formula
Uttar Pradesh Board · Class 9 · Mathematics
Flashcards for Heron's Formula — Uttar Pradesh Board Class 9 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
What is Heron's Formula and when is it used?
Answer
Heron's Formula is used to find the area of a triangle when all three sides are known but the height is not given. It is particularly useful for scalene triangles where calculating height is difficult
Who was Heron and what was his contribution to mathematics?
Answer
Heron was born around 10 AD, possibly in Alexandria, Egypt. He was an encyclopedic writer in mathematics and physics. He worked on mensuration problems and derived the famous formula for calculating t
State Heron's Formula mathematically.
Answer
Heron's Formula: Area of triangle = √[s(s-a)(s-b)(s-c)], where a, b, and c are the sides of the triangle, and s is the semi-perimeter = (a+b+c)/2
What is semi-perimeter? How is it calculated?
Answer
Semi-perimeter (s) is half the perimeter of a triangle. It is calculated as: s = (a+b+c)/2, where a, b, and c are the three sides of the triangle. It is a key component in Heron's Formula.
A triangular park has sides 40 m, 32 m, and 24 m. Calculate its semi-perimeter.
Answer
Given: a = 40 m, b = 32 m, c = 24 m Semi-perimeter s = (a+b+c)/2 = (40+32+24)/2 = 96/2 = 48 m
Using the triangular park example (sides 40 m, 32 m, 24 m), find the area using Heron's Formula.
Answer
Given: a = 40 m, b = 32 m, c = 24 m, s = 48 m s-a = 48-40 = 8 m s-b = 48-32 = 16 m s-c = 48-24 = 24 m Area = √[48×8×16×24] = √[147456] = 384 m²
How can you verify if the triangular park (40 m, 32 m, 24 m) forms a right triangle?
Answer
Check if a² + b² = c² for the largest side as hypotenuse: 32² + 24² = 1024 + 576 = 1600 40² = 1600 Since 32² + 24² = 40², it is a right triangle with 40 m as hypotenuse.
For a right triangle with sides 32 m, 24 m, and 40 m, verify the area using both traditional method and Heron's Formula.
Answer
Traditional method: Area = (1/2) × base × height = (1/2) × 32 × 24 = 384 m² Heron's Formula: Area = √[48×8×16×24] = 384 m² Both methods give the same result, confirming the accuracy of Heron's Formula
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