Heron's Formula
Gujarat Board · Class 9 · Mathematics
Flashcards for Heron's Formula — Gujarat Board Class 9 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
What is Heron's Formula and who discovered it?
Answer
Heron's Formula (also called Hero's Formula) was discovered by Heron of Alexandria around 10 AD. It calculates the area of a triangle when all three sides are known, without needing to find the height
State Heron's Formula for finding the area of a triangle.
Answer
Heron's Formula: Area = √[s(s-a)(s-b)(s-c)] where: • a, b, c are the three sides of the triangle • s is the semi-perimeter = (a+b+c)/2 • The result gives the area in square units
What is semi-perimeter? How do you calculate it?
Answer
Semi-perimeter (s) is half of the perimeter of a triangle. Formula: s = (a+b+c)/2 where a, b, c are the three sides of the triangle. Example: If sides are 6 cm, 8 cm, 10 cm, then s = (6+8+10)/2 = 12 c
When is Heron's Formula most useful?
Answer
Heron's Formula is most useful when: • All three sides of a triangle are known • The height of the triangle is difficult to calculate • You cannot easily identify a base and corresponding height • Wor
Find the area of a triangle with sides 3 cm, 4 cm, and 5 cm using Heron's Formula.
Answer
Given: a = 3 cm, b = 4 cm, c = 5 cm Step 1: Calculate semi-perimeter s = (3+4+5)/2 = 6 cm Step 2: Apply Heron's Formula Area = √[s(s-a)(s-b)(s-c)] = √[6(6-3)(6-4)(6-5)] = √[6×3×2×1] = √36 = 6 cm²
A triangular park has sides 40 m, 32 m, and 24 m. Find its area using Heron's Formula.
Answer
Given: a = 40 m, b = 32 m, c = 24 m Step 1: s = (40+32+24)/2 = 48 m Step 2: s-a = 48-40 = 8 m s-b = 48-32 = 16 m s-c = 48-24 = 24 m Step 3: Area = √[48×8×16×24] = √[147456] = 384 m² Note: This is a ri
Find the area of an equilateral triangle with side 10 cm using Heron's Formula.
Answer
Given: All sides = 10 cm (a = b = c = 10) Step 1: s = (10+10+10)/2 = 15 cm Step 2: s-a = s-b = s-c = 15-10 = 5 cm Step 3: Area = √[15×5×5×5] = √[1875] = 25√3 cm² ≈ 25×1.732 = 43.3 cm²
Two sides of a triangle are 8 cm and 11 cm, and the perimeter is 32 cm. Find the area.
Answer
Given: a = 8 cm, b = 11 cm, Perimeter = 32 cm Step 1: Find third side c = 32 - (8+11) = 13 cm Step 2: s = 32/2 = 16 cm Step 3: s-a = 8, s-b = 5, s-c = 3 Step 4: Area = √[16×8×5×3] = √[1920] = 8√30 cm²
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